Bidirectionally Coupled Research Articles

Two-way coupling between ice flow and channelized subglacial drainage enhances modeled marine-ice-sheet retreat

Abstract. Ice-sheet models used to predict sea-level rise often neglect subglacial hydrology. However, theory and observations suggest that ice flow and subglacial water flow are bidirectionally coupled: ice geometry affects hydraulic potential, hydraulic potential modulates basal shear stress via the basal water pressure, and ice flow advects the subglacial drainage system. This coupling could impact rates of ice mass change but remains poorly understood. We develop a coupled ice–subglacial-hydrology model to investigate the effects of coupling on the long-term evolution of marine-terminating ice sheets. We combine a one-dimensional channelized subglacial hydrology model with a depth-integrated marine-ice-sheet model, incorporating each component of the coupling listed above, yielding a set of differential equations that we solve using a finite-difference, implicit time-stepping approach. We conduct a series of experiments with this model, using either bidirectional or unidirectional coupling. These experiments generate profiles of channel cross-sectional area, channel flow rate, channel effective pressure, ice thickness, and ice velocity. We discuss how the profiles shape one another, resulting in the effective pressure reaching a local maximum in a region near the grounding line. We also describe the impact of bidirectional coupling on the transient retreat of ice sheets through a comparison of our coupled model with ice-flow models that have imposed static basal conditions. We find that including coupled subglacial hydrology leads to grounding-line retreat that is virtually absent when static basal conditions are assumed. This work highlights the role time-evolving subglacial drainage may have in ice-sheet change and informs efforts to include it in ice-sheet models. This work also supplies a physical basis for a commonly used parameterization which assumes that the subglacial water pressure is set by the bed's depth beneath the sea surface.

Bidirectional coupling in fractional order maps of incommensurate orders

We study the stability of bidirectionally coupled integer and fractional-order maps. The system is further generalized to the case where both the equations have fractional order difference operators. We derive stability conditions for the synchronized fixed point in both cases. We show that this formalism can be extended to inhomogeneous systems of N coupled map where any map can be of arbitrary fractional order or integer order. We give a solution to a specific case of a system with periodic disorder where alternate maps are of integer and fractional order or different fractional orders.

Interaction of a Ventricular Assist Device With Patient-Specific Cardiovascular Systems: In-Silico Study With Bidirectional Coupling.

Ventricular assist devices (VADs) are used to assist the heart function of patients with advanced heart failure. Computational fluid dynamics in VADs are widely applied in the development and optimization, for example, to evaluate blood damage. For these simulations, the pulsating operating conditions, in which the VAD operates, should be included accurately. Therefore, this study aims to evaluate the flow in a VAD by interacting with patient-specific cardiovascular systems of heart failure patients. A numeric method will be presented, which includes a patient-specific cardiovascular system model that is bidirectionally coupled with a three-dimensional (3D) flow simulation of the HeartMate 3. The cardiovascular system is represented by a lumped parameter model. Three heart failure patients are considered, based on clinical data from end-stage heart failure patients. Various parameters of the cardiovascular system and the VAD are analyzed, for example, flow rates, pressures, VAD heads, and efficiencies. A further important parameter is the blood damage potential of the VAD, which varies significantly among different patients. Moreover, the predicted blood damage fluctuates within a single heartbeat. The increase in blood damage is evaluated based on the operating conditions. Both, overload and especially partial load conditions during the pulsating operation result in elevated blood damage.

Effects of electric field on vibrational resonance in Izhikevich neuronal systems

In this paper, based on the Izhikevich neuron model, the effects of electric field (EF) on vibrational resonance (VR) of single neuron and bidirectionally coupled neurons system are investigated. It is found that multiple vibrational resonances (MVR) can be observed in a single Izhikevich neuron model whether EF is considered or not. After the introduction of EF, the system exhibits worse MVR and local vibrational anti-resonance can be observed. In coupled neuronal system, the effect of bidirectional coupling causes MVR to disappear and the system only exhibits the phenomenon of VR. When EF is not considered, the vibrational anti-resonance is also observed. Interestingly, the introduction of EF weakens both VR and anti-resonance in the system. In addition, the effects of system parameters such as the EF strength controller and coupling strength on the Fourier coefficients are also investigated, and it is found that these parameters can also cause changes in the number of resonance peaks, resulting in vibrational bi-resonance and vibrational triple-resonance. The EF plays an important role in attenuating VR in neuronal systems. Therefore, this study can provide new insights for further control of abnormal electrical activities and information transmission in neurons.

Automated bidirectional coupling of multiscale models of aerosol dosimetry: Validation with subject-specific deposition data

Assessing the toxicity of airborne particulate matter or the efficacy of inhaled drug depends upon accurate estimates of deposited fraction of inhaled materials. In silico approaches can provide important insights into site- or airway-specific deposition of inhaled aerosols in the respiratory system. In this study, we improved on our recently developed 3D/1D model that simulate aerosol transport and deposition in the whole lung over multiple breath cycles (J. Aerosol Sci 151:105647). A subject-specific multiscale lung model of a healthy male subject using computational fluid-particle dynamics (CFPD) in a 3D model of the oral cavity through the large bronchial airways entering each lobe was bidirectionally coupled with a recently improved Multiple Path Particle Dosimetry (MPPD) model to predict aerosol deposition over the entire respiratory tract over multiple breaths for four conditions matching experimental aerosol exposures in the same subject from which the model was developed. These include two particle sizes (1 and 2.9 μm) and two subject-specific breathing rates of ∼300 ml/s (slow breathing) and ∼750 ml/s (fast breathing) at a target tidal volume of 1 L. In silico predictions of retained fraction were 0.31 and 0.29 for 1 μm and 0.66 and 0.62 for 2.9 μm during slow and fast breathing, respectively, and compared well with experimental data (1 μm: 0.31 ± 0.01 (slow) and 0.27 ± 0.01 (fast), 2.9 μm: 0.63 ± 0.03 (slow) and 0.68 ± 0.02 (fast)). These results provide a great deal of confidence in the validity and reliability of our approach.

Multiscroll in Bidirectionally Coupled Jerk Oscillators: Theoretical Analysis and PSpice Verification

It is known that the unidirectional coupling between a double-scroll system (drive) in the oscillation regime with another system (response) in the steady-state, gives rise to more complex dynamics such as multiscroll attractors [Dana et al., 2008]. This paper shows the way to move from n-scroll to 2n-scroll in a bidirectional coupling scheme between two jerk oscillators. The coupling considered can be interpreted as a perturbation to each oscillator’s amplitude through a signal proportional to the amplitude of the other. Indeed, starting from a situation of two oscillators which can generate double-scroll dynamics individually, we perform a bidirectional coupling of both oscillators which results in more complex dynamics such as multistability and 4-scroll chaotic attractor in the coupled system (not observed in an isolated oscillator). The underlined coupling scheme provides an efficient method for generating higher-order multiscroll attractors. The route to the 4-scroll chaotic attractor is explained with the help of bifurcation diagrams, plots of several phase portraits, and basins of attractions. Indirect validation of the theoretical analysis is carried out by using the PSpice simulation software.

Coupled Electromagnetic-Dynamic Modeling and Bearing Fault Characteristics of Induction Motors considering Unbalanced Magnetic Pull

Induction motors are complex energy conversion systems across the domains of dynamics, electricity, and magnetism. Most existing models mainly consider unidirectional coupling, such as the effect of dynamics on electromagnetic properties, or the effect of unbalanced magnetic pull on dynamics, while in practice it should be a bidirectional coupling effect. The bidirectionally coupled electromagnetic-dynamics model is beneficial to the analysis of induction motor fault mechanisms and characteristics. This paper proposes a coupled electromagnetic-dynamic modeling method that introduces unbalanced magnetic pull. By using the rotor velocity, air gap length, and unbalanced magnetic pull as the coupling parameters, the coupled simulation of the dynamic and electromagnetic models can be effectively realized. Simulation results for bearing faults show that the introduction of magnetic pull induces a more complex dynamic behavior of the rotor, which in turn leads to modulation in the vibration spectrum. The fault characteristics can be found in the frequency domain of the vibration and current signals. Through the comparison between simulation and experimental results, the effectiveness of the coupled modeling approach and the frequency domain characteristics caused by the unbalanced magnetic pull are verified. The proposed model can help to obtain a variety of information that is difficult to measure in reality and can also serve as a technical basis for further research on nonlinear characteristics and chaos in induction motors.

Synchronization of spatially discordant voltage and calcium alternans in cardiac tissue.

The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

Bi-Directional System Coupling for Conjugate Heat Transfer and Variable Leakage Gap CFD Analysis of Twin-Screw Compressors

Oil-free twin-screw compressors are essential in various industrial applications where clean compressed gas is required. Due to the absence of the cooling oil in these machines, thermal deformations are large. Hence, design clearances are generally set at a relatively large value of more than 150 μm. Leakage through these clearances are the primary source of flow loss. It is essential to predict the change of the gap size in operation accurately so that the design clearances can be minimised, allowing reliable operation and maximising compressor efficiency. To achieve this, CFD and Structural solvers were combined. The CFD model uses a single domain deforming grid of the twin-screw rotors generated in SCORG grid generator, together with ANSYS CFX flow solver. The thermal model of the rotors and housing uses ANSYS Structural solver. Two modelling systems were coupled bi-directionally to obtain variation in the radial leakage gap size for calculation of performance in the CFD model. The predicted compressor performance thus obtained was compared with measurements of flow, internal pressure-rise, power, specific power, volumetric and adiabatic efficiency. For the test case, three variations of radial gap size were evaluated, two of them with the uniform gap size of 10 μm and 160 μm and the third one with a variable gap size as predicted by the bi-directionally coupled model. The coupled model predicted this gap size to vary from 24 to 117 μm, thus predicting an improved flow and volumetric efficiency by 8.2%, lower indicated power by 2.5% and a higher adiabatic efficiency by 5.5%, in comparison to the design gap size of 160 μm. These predicted gap sizes could be used to improve the design clearances of the compressor by reducing them from 160 to 120 μm which would result in a better performance during operation.

A Novel Approach to Carrying Capacity: Froma prioriPrescription toa posterioriDerivation Based on Underlying Mechanisms and Dynamics

The Human System is within the Earth System. They should be modeled bidirectionally coupled, as they are in reality. The Human System is rapidly expanding, mostly due to consumption of fossil fuels (approximately one million times faster than Nature accumulated them) and fossil water. This threatens not only other planetary subsystems but also the Human System itself. Carrying Capacity is an important tool to measure sustainability, but there is a widespread view that Carrying Capacity is not applicable to humans. Carrying Capacity has generally been prescribed a priori, mostly using the logistic equation. However, the real dynamics of human population and consumption are not represented by this equation or its variants. We argue that Carrying Capacity should not be prescribed but should insteadbe dynamically derived a posteriori from the bidirectional coupling of Earth System submodels with the Human System model. We demonstrate this approach with a minimal model of Human–Nature interaction (HANDY). ▪ The Human System is a subsystem of the Earth System, with inputs (resources) from Earth System sources and outputs (waste, emissions) to Earth System sinks. ▪ The Human System is growing rapidly due to nonrenewable stocks of fossil fuels and water and threatens the sustainability of the Human System and to overwhelm the Earth System. ▪ Carrying Capacity has been prescribed a priori and using the logistic equation, which does not represent the dynamics of the Human System. ▪ Our new approach to human Carrying Capacity is derived from dynamically coupled Earth System–Human System models and can be used to estimate the sustainability of the Human System.

Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation.

Spontaneous sub-cellular calcium release events (SCRE) are conjectured to promote rapid arrhythmias associated with conditions such as heart failure and atrial fibrillation: they can underlie the emergence of spontaneous action potentials in single cells which can lead to arrhythmogenic triggers in tissue. The multi-scale mechanisms of the development of SCRE into arrhythmia triggers, and their dynamic interaction with the tissue substrate, remain elusive; rigorous and simultaneous study of dynamics from the nanometre to the centimetre scale is a major challenge. The aim of this study was to develop a computational approach to overcome this challenge and study potential bi-directional coupling between sub-cellular and tissue-scale arrhythmia phenomena. A framework comprising a hierarchy of computational models was developed, which includes detailed single-cell models describing spatio-temporal calcium dynamics in 3D, efficient non-spatial cell models, and both idealised and realistic tissue models. A phenomenological approach was implemented to reproduce SCRE morphology and variability in the efficient cell models, comprising the definition of analytical Spontaneous Release Functions (SRF) whose parameters may be randomly sampled from appropriate distributions in order to match either the 3D cell models or experimental data. Pro-arrhythmogenic pacing protocols were applied to initiate re-entry and promote calcium overload, leading to the emergence of SCRE. The SRF accurately reproduced the dynamics of SCRE and its dependence on environment variables under multiple different conditions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations after termination. A purely functional mechanism of re-entry and focal activity localisation was demonstrated, related to the unexcited spiral wave core. In conclusion, a novel approach has been developed to dynamically model SCRE at the tissue scale, which facilitates novel, detailed multi-scale mechanistic analysis. It was revealed that complex re-entrant excitation patterns and SCRE may be bi-directionally coupled, promoting novel mechanisms of arrhythmia perpetuation.

A magnetohydrodynamic numerical model with external circuit coupled for pulsed inductive thrusters

Pulsed inductive thruster, which employs pulsed inductive magnetic field to ionize propellant and accelerate a bulk of plasma, is accompanied with complicated phenomena such as plasma physics, magnetohydrodynamics and the strong coupling effect between the drive-circuit and plasma load. Simulations employing a snowplow circuit model or present magnetohydrodynamic model might be insufficient to capture these important phenomena simultaneously and self-consistently. Therefore the validity of currently existing numerical models remain to be verified. In this paper, a novel circuit-coupled magnetohydrodynamic model is proposed. The flow process of the plasma in the acceleration channel and the discharge process of the circuit are solved simultaneously in a bi-directionally coupled method by calculating the voltage drop across the drive-coil according to the drive-coil geometry and the temporal electric field distribution. The magnetohydrodynamic field is solved with Navier-Stokes equations coupled with Maxwell equations, while the plasma thermodynamic parameters and transport parameters are calculated by employing the local thermal equilibrium model. And the circuit process is solved with a set of circuit equations based on Kirchhoff's law. All the physics fields are computed by the finite element method in COMSOL MultiphysicsTM. Numerical simulation for American TRW Inc.'s MK-1 thruster successfully reproduces its working process. The numerical magnetic field distribution in plasma, the time-dependent collective Lorentz force and the specific impulse and efficiency of the thruster under varying working voltages agree well with the corresponding experimental data. Numerical results imply that a compact azimuthal plasma current sheet is established in the initial 1-2 s in the near-face region of the drive-coil. This plasma current sheet, which entrains the majority of the propellant, is excluded and accelerated by the Lorentz force derived from the drive-coil magnetic field. Most of the propellant acceleration is accomplished within the first half period of the circuit current, which is about 7-8 s. Furthermore, the bi-directional coupling effect is quantitatively analyzed with the current model. Numerical results indicate that the coupling plasma load generally tends to increase the effective resistance and reduce the effective inductance of the drive-circuit. Moreover, this effect changes as the plasma structure varies. When the plasma current sheet moves away from the drive-coil, the mutual inductance between plasma load and drive-coil decreases monotonically. That implys that the plasma current sheet decouples gradually from the dirve-circuit in the process. In conclusion, bidirectional coupling effect between plasma load and drive-circuit plays an important role in the operation of the thruster. This model could be used to predict the performances of pulsed inductive thrusters and might be helpful in designing a more effective thruster.

On Applicability of Auxiliary System Approach to Detect Generalized Synchronization in Complex Network

Generalized synchronization is ubiquitous in nature. It is well known that the auxiliary system approach has been widely used to verify the presence of generalized synchronization. This approach was firstly proposed in a drive-response system, then extended to the bidirectionally coupled systems and complex networks. However, the well-known generalized auxiliary system method lacks a rigorous theoretical basis for its various applications. Two recent counterexamples indicate us the inapplicability of this method. Inspired by the counterexamples, we find that it is interesting to ask the following two fundamental questions: i) Why is the generalized auxiliary system approach unworkable in the networks with bidirectional couplings? ii) Are there any essential conditions for the applications of this approach? This technical note aims at establishing a rigorous theoretical basis for the applicability of auxiliary system approach. That is, the generalized auxiliary system approach is effective only if there does not exist any path from nodes to their driving neighbors (who drive these nodes) in a network. Several representative examples are also given to validate our theoretical results.

Highly Correlated Chaotic Emission From Bidirectionally Coupled Semiconductor Lasers

Optically coupled semiconductor lasers (SLs) are known to exhibit chaotic properties in their emitted signals. Depending on the number of SLs and the coupling topology, their emissions can potentially show stable, synchronized behavior. The level of synchrony depends on numerous parameters and is the key factor to design secure communication systems based on synchronized chaotic signals. In this work we investigate a bidirectional coupling topology, with two or more SLs coupled with a common hub SL, which leads to an unprecedented level of synchronization. Cross-correlation (CC) values as high as 0.9961 are reported between SLs, when the latter operate at a fully chaotic regime and with spectral emission profiles that show minimized periodicities. Such conditions promote the proposed topology for cryptographic applications.

Effects of self-coupling and asymmetric output on metastable dynamical transient firing patterns in arrays of neurons with bidirectional inhibitory coupling

Metastable dynamical transient patterns in arrays of bidirectionally coupled neurons with self-coupling and asymmetric output were studied. First, an array of asymmetric sigmoidal neurons with symmetric inhibitory bidirectional coupling and self-coupling was considered and the bifurcations of its steady solutions were shown. Metastable dynamical transient spatially nonuniform states existed in the presence of a pair of spatially symmetric stable solutions as well as unstable spatially nonuniform solutions in a restricted range of the output gain of a neuron. The duration of the transients increased exponentially with the number of neurons up to the maximum number at which the spatially nonuniform steady solutions were stabilized. The range of the output gain for which they existed reduced as asymmetry in a sigmoidal output function of a neuron increased, while the existence range expanded as the strength of inhibitory self-coupling increased. Next, arrays of spiking neuron models with slow synaptic inhibitory bidirectional coupling and self-coupling were considered with computer simulation. In an array of Class 1 Hindmarsh–Rose type models, in which each neuron showed a graded firing rate, metastable dynamical transient firing patterns were observed in the presence of inhibitory self-coupling. This agreed with the condition for the existence of metastable dynamical transients in an array of sigmoidal neurons. In an array of Class 2 Bonhoeffer–van der Pol models, in which each neuron had a clear threshold between firing and resting, long-lasting transient firing patterns with bursting and irregular motion were observed.

The impact of surgical excisions on human gastric slow wave conduction, defined by high-resolution electrical mapping and in silico modeling.

Gastric contractions are coordinated by slow waves, generated by interstitial cells of Cajal (ICC). Gastric surgery affects slow wave conduction, potentially contributing to postoperative gastric dysfunction. However, the impact of gastric cuts on slow waves has not been comprehensively evaluated. This study aimed to define consequences of surgical excisions on gastric slow waves by applying high-resolution (HR) electrical mapping and in silico modeling. Patients undergoing gastric stimulator implantation (n=10) underwent full-thickness stapled excisions (25×15mm, distal corpus) for histological evaluation, enabling HR mapping (256 electrodes; 36cm(2) ) over and adjacent to excisions. A biophysically based in silico model of bidirectionally coupled ICC networks was developed and applied to investigate the underlying conduction mechanisms and importance of excision orientation. Normal gastric slow waves propagated aborally (3.0±0.2 cpm). Excisions induced complete conduction block and wavelets that rotated around blocks, then propagated rapidly circumferentially distal to the blocks (8.5±1.2 vs normal 3.6±0.4mm/s; p< 0.01). This 'conduction anisotropy' homeostatically restored antegrade propagating gastric wavefronts distal to excisions. Excisions were associated with complex dysrhythmias in five patients: retrograde propagation (3/10), ectopics (3/10), functional blocks (2/10), and collisions (1/10). Simulations demonstrated conduction anisotropy emerged from bidirectional coupling within ICC layers and showed transverse incision length and orientation correlated with the degree of conduction distortion. Orienting incisions in the longitudinal gastric axis causes least disruption to electrical conduction and motility. However, if transverse incisions are made, a homeostatic mechanism of gastric conduction anisotropy compensates by restoring aborally propagating wavefronts. Complex dysrhythmias accompanying excisions could modify postoperative recovery in susceptible patients.

Complex Early and Delayed Afterdepolarization Dynamics caused by Voltage-Calcium Coupling in Cardiac Myocytes

Please cite this article in press as: Song et al., Calcium-Voltage Coupling in the Genesis of Early and Delayed Afterdepolarizations in Cardiac Myocytes, Bio- physical Journal (2015), http://dx.doi.org/10.1016/j.bpj.2015.03.011 Biophysical Journal Volume 108 April 2015 1–14 Article Calcium-Voltage Coupling in the Genesis of Early and Delayed Afterdepolarizations in Cardiac Myocytes Zhen Song, 1,2 Christopher Y. Ko, 1,2 Michael Nivala, 1,2 James N. Weiss, 1,2,3 and Zhilin Qu 1,2, * Cardiovascular Research Laboratory, 2 Department of Medicine (Cardiology), and 3 Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, California ABSTRACT Early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) are voltage oscillations known to cause cardiac arrhythmias. EADs are mainly driven by voltage oscillations in the repolarizing phase of the action potential (AP), while DADs are driven by spontaneous calcium (Ca) release during diastole. Because voltage and Ca are bidirectionally coupled, they modulate each other’s behaviors, and new AP and Ca cycling dynamics can emerge from this coupling. In this study, we performed computer simulations using an AP model with detailed spatiotemporal Ca cycling incorporating stochastic openings of Ca channels and ryanodine receptors to investigate the effects of Ca-voltage coupling on EAD and DAD dynamics. Simulations were complemented by experiments in mouse ventricular myocytes. We show that: 1) alteration of the Ca transient due to increased ryanodine receptor leakiness and/or sarco/endoplasmic reticulum Ca ATPase activity can either promote or suppress EADs due to the complex effects of Ca on ionic current properties; 2) spontaneous Ca waves also exhibit complex effects on EADs, but cannot induce EADs of significant amplitude without the participation of I Ca,L ; 3) lengthening AP duration and the occurrence of EADs promote DADs by increasing intracellular Ca loading, and two mechanisms of DADs are identified, i.e., calcium-wave-dependent and a calcium-wave-independent; and 4) Ca-voltage coupling promotes complex EAD patterns such as EAD alternans that are not observed for solely voltage-driven EADs. In conclusion, Ca-voltage coupling combined with the nonlinear dynamical behaviors of voltage and Ca cycling play a key role in generating complex EAD and DAD dynamics observed experimentally in cardiac myocytes, whose mechanisms are complex but analyzable. INTRODUCTION Early afterdepolarizations (EADs) and delayed afterdepola- rizations (DADs) are known to cause arrhythmias in a vari- ety of cardiac diseases, including long QT syndromes (1–3), catecholaminergic polymorphic ventricular tachycardia (CPVT) (4,5), and heart failure (6,7). EADs are voltage oscillations that occur during the repolarizing phases of the action potential (AP). By prolonging the AP duration (APD) regionally, EADs can increase dispersion of refracto- riness, forming a tissue substrate vulnerable to reentry. Furthermore, if EADs reach the threshold to propagate out this region as premature ventricular contractions, they can serve as triggers to induce reentry. DADs, on the other hand, are voltage oscillations during diastole. By depolariz- ing the resting membrane potential regionally, DADs can cause conduction block (8), and, if they reach the threshold for sodium (Na) channel activation, can generate triggered activity (TA) manifesting as premature ventricular contrac- tions that induce reentry. EADs occur in the setting of reduced repolarization reserve, such as long QT syndromes, and have classically been attributed to voltage-driven oscillations in the repola- rizing phase of the AP, although spontaneous sarcoplasmic Submitted October 29, 2014, and accepted for publication March 10, 2015. *Correspondence: zqu@mednet.ucla.edu reticulum (SR) calcium (Ca) release has also been proposed as an important mechanism. DADs, on the other hand, are promoted by Ca cycling disorders, such as CPVT and digi- talis toxicity, which promote Ca-driven oscillations. Heart failure represents a combination of reduced repolarization reserve and abnormal Ca cycling resulting from electrical and excitation-contraction coupling remodeling processes driven by both genetic transcriptional and posttranslational signaling components. In all of these settings, it is common for EADs and DADs to coexist and influence each other. This is because membrane voltage is strongly affected by Ca-sensitive ionic currents, and, conversely, cellular Ca loading is strongly influenced by voltage-dependent ionic currents, referred to as bidirectional Ca-voltage coupling. Ca-voltage coupling can promote complex AP dynamics in the heart (9). Analyzing the interactions between EADs and DADs (and voltage and Ca-cycling coupling dynamics in general), however, has been challenging, because the Ca cycling dynamics (e.g., Ca waves and oscillations) result from a spatially distributed heterogeneous network of Ca release units (CRUs) in the cell. The Ca waves emanating from various subcellular regions integrate to depolarize dia- stolic membrane voltage by activating Ca-sensitive inward currents including the Na-Ca exchange (NCX) current (I NCX ) and Ca-activated nonselective cation channels (I ns(Ca) ), generating DADs. Similarly, spontaneous SR Ca Editor: Randall Rasmusson. O 2015 by the Biophysical Society http://dx.doi.org/10.1016/j.bpj.2015.03.011 BPJ 6468

Projective synchronization of chaotic systems with bidirectional nonlinear coupling

This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.

Bidirectionally Coupled Network and Road Traffic Simulation for Improved IVC Analysis

Recently, many efforts have been made to develop more efficient Inter-Vehicle Communication (IVC) protocols for on-demand route planning according to observed traffic congestion or incidents, as well as for safety applications. Because practical experiments are often not feasible, simulation of network protocol behavior in Vehicular Ad Hoc Network (VANET) scenarios is strongly demanded for evaluating the applicability of developed network protocols. In this work, we discuss the need for bidirectional coupling of network simulation and road traffic microsimulation for evaluating IVC protocols. As the selection of a mobility model influences the outcome of simulations to a great extent, the use of a representative model is necessary for producing meaningful evaluation results. Based on these observations, we developed the hybrid simulation framework Veins (Vehicles in Network Simulation), composed of the network simulator OMNeT++ and the road traffic simulator SUMO. In a proof-of-concept study, we demonstrate its advantages and the need for bidirectionally coupled simulation based on the evaluation of two protocols for incident warning over VANETs. With our developed methodology, we can advance the state-of-the-art in performance evaluation of IVC and provide means to evaluate developed protocols more accurately.

Bidirectionally coupled synchronization of the generalized Lorenz systems

Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.