Synchronization Regime Research Articles

Collective firing patterns of neuronal networks with short-term synaptic plasticity.

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

Synchronization Regimes in an Ensemble of the Phase Oscillators Coupled Through a Diffusion Field

Synchronization Regimes in an Ensemble of the Phase Oscillators Coupled Through a Diffusion Field

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.

Indirect estimation of state variables of industrial reaction-regeneration systems based on computer simulation

A reaction-regeneration system is described, which is a hardware part of industrial production and is characterized by an exceptional feature – pronounced nonlinearity in the form of a plurality of stationary solutions of model differential equations. This feature forces one to resort to engineering solutions that are alternative to direct measurements. The problem of indirect estimation of the components of the state vector of the reaction-regeneration system is considered. The incorrectness of the indirect assessment of the state of such objects on the basis of the theory of Kalman filters is shown. The incorrectness is due to the ambiguity of the mapping of the state space into the space of vectors tangent to the trajectories. An approach based on synchronous simulation in dynamics is proposed, which consists in comparing two evolutions “object – model” with minimization of the mismatch. A technique based on the inclusion of the second derivatives of the state variables into the mismatch function is presented. The methodology of the sensitivity of indirect estimation systems based on maximizing the similarity of the compared evolutions “object – model” in the regime of strict synchronization with respect to external disturbances and control levers is considered. It is shown that the accuracy of the indirect estimation of physically unmeasurable coordinates is largely determined by the mathematical aspects of minimizing the mismatch function, which, due to the multiplicity of solutions to model equations, has a complex structure of the response surface.

Modal synchronization of coupled bistable van der Pol oscillators

The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.

Flow-induced vibrations of a hinged cavity at the rear of a blunt-based body subject to laminar flow

We perform numerical simulations to characterize the flow-induced vibrations (FIV) of a rear cavity with elastically hinged rigid plates, placed as a passive device at the base of a blunt body that is subject to a laminar flow of Reynolds number Re=400. The dynamic response and forcing of plates, wake features and force coefficients are investigated for the range of reduced velocity U*=[0,30]. Three different regimes of the rotational oscillations are identified. An initial branch of low oscillation amplitude is defined for U*<2.5, where the plates oscillate in counter-phase (varicose mode) with a frequency fp that corresponds to the harmonic of the wake vortex shedding frequency fp≃2fw, and is similar to the natural frequency of the plates, fp≃fn. For intermediate values of U*, the plates oscillate in phase (sinuous mode) at their natural frequency, with respect to a closer averaged location of plates. Such synchronization regime amplifies the vibration magnitude and defines the upper branch in the amplitude response curve, whose maximum is attained at U*=4.7. Due to such enhanced vibration, the vortex shedding frequency is now locked-in at the natural frequency of plates, so that fp=fn=fw. Finally, for larger values of U*, a lower branch of moderate amplitude response is defined, which is characterized by the in-phase oscillation of plates, with respect to an more open average position, governed again by the shedding frequency, fp=fw>fn. Additionally, a multibody model has been developed to retrieve, from the plates rotational motion, the resultant forces and moments that produce the plates vibration. Such inverse dynamics model is formulated to allow its generalization for configurations of higher dynamical order, and validated against the results obtained from the numerical simulations. The analysis shows that the synchronization regime is mainly promoted by a reduced fluid damping and a forcing moment that acts in phase with the plates motion. The switch in such phase from 0∘ to 180∘ occurs after the lock-in, what attenuates the plates response at large U*. In general, the FIV of plates alters the vortex shedding and near wake pressure, especially during the synchronization regime, inducing an overall increase of the global force coefficients with respect to the static cavity. Thus, the performance of hinged plates enhances generally the mean drag, although a 25% reduction is reported for the lift amplitude.

Adversarial decision strategies in multiple network phased oscillators: The Blue-Green-Red Kuramoto-Sakaguchi model

We consider a model of three interacting sets of decision-making agents, labeled Blue, Green and Red, represented as coupled phased oscillators subject to frustrated synchronisation dynamics. The agents are coupled on three networks of differing topologies, with interactions modulated by different cross-population frustrations, internal and cross-network couplings. The intent of the dynamic model is to examine the degree to which two of the groups of decision-makers, Blue and Red, are able to realise a strategy of being ahead of each others’ decision-making cycle while internally seeking synchronisation of this process – all in the context of further interactions with the third population, Green. To enable this analysis, we perform a significant dimensional reduction approximation and stability analysis. We compare this to a numerical solution for a range of internal and cross-network coupling parameters to investigate various synchronisation regimes and critical thresholds. The comparison reveals good agreement for appropriate parameter ranges. Performing parameter sweeps, we reveal that Blue’s pursuit of a strategy of staying too-far ahead of Red’s decision cycles triggers a second-order effect of the Green population being ahead of Blue’s cycles. This behaviour has implications for the dynamics of multiple interacting social groups with both cooperative and competitive processes.

On the initiation and sustenance of flow-induced vibration of cylinders: insights from force partitioning

Abstract

Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise.

We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.

Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators

A problem of mathematical modeling and analysis of complex oscillatory behavior in coupled nonlinear stochastic systems is considered. We study stochastic bifurcations and transitions between in-phase and anti-phase dynamics in two coupled map-based neural oscillators with regular and chaotic attractors. Interesting dynamical regimes of isolated and coupled oscillators are considered in a wide range of both deterministic and stochastic modes associated with in-phase and anti-phase synchronization. The comprehensive nonlinear and stochastic analyses using a stochastic sensitivity approach and confidence ellipses allowed us to reveal the geometry of multiple basins of attraction of coexisting states and confidence areas in both synchronous and asynchronous regimes. Coupling-induced and noise-induced transitions between order and chaos are also discussed.

Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag.

Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.

Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators.

The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.

Flow-induced transverse vibration of an elliptical cylinder with different aspect ratios

This paper presents numerical investigations of the flow-induced vibration of an elastically mounted elliptical cylinder with different aspect ratios. The cylinder is constrained to vibrate only in the cross-flow direction, with the major axis being perpendicular to the uniform flow. The Reynolds number, based on the free stream velocity and the major axis width, is fixed as 100. The aspect ratio (AR) is based on the minor axis width over the major axis width. By specifying AR = 0.1, 0.25, 0.5, 0.75 and 1, with a fixed mass ratio of 10, the fluid–cylinder interactions are simulated using a high-order Spectral/hp element method to characterize the vibration responses, oscillation frequencies, fluctuating drag and lift coefficients, lock-in regimes and vorticity contours, with the variation of reduced velocities. A synchronization regime is found to be directly correlated with AR. For the lowest AR = 0.1, the elliptical cylinder response is found to be greater, as much as twice, than the circular cylinder response, by also exhibiting an earlier onset of the lock-in. The lack of the cylinder afterbody has a significant effect on the lower-branch response, resulting in a beating phenomenon and a rapid reduction in the response with decreasing AR. The effect of varying mass ratios is also investigated for low AR cases. The vortex shedding modes for all the response branches are found to be 2S with wake variants. A parallel vortex-shedding mode is noticed in a lower AR case with a large-amplitude oscillation whereas the C(2S) mode is observed in a higher AR case.

Exceptional Point of Degeneracy in a Backward-Wave Oscillator with Distributed Power Extraction

We show how an exceptional point of degeneracy (EPD) is formed in a system composed of an electron beam interacting with an electromagnetic mode guided in a slow wave structure (SWS) with distributed power extraction from the interaction zone. Based on this kind of EPD, a new regime of operation is devised for backward wave oscillators (BWOs) as a synchronous and degenerate regime between a backward electromagnetic mode and the charge wave modulating the electron beam. Degenerate synchronization under this EPD condition means that two complex modes of the interactive system do not share just the wavenumber, but they rather coalesce in both their wavenumbers and eigenvectors (polarization states). In principle this new condition guarantees full synchronization between the electromagnetic wave and the beam's charge wave for any amount of output power extracted from the beam, setting the threshold of this EPD-BWO to any arbitrary, desired, value. Indeed, we show that the presence of distributed radiation in the SWS results in having high-threshold electron-beam current to start oscillations which implies higher power generation. These findings have the potential to lead to highly efficient BWOs with very high output power and excellent spectral purity.

Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents

We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations leads to the possibility of existence of asymptotically stable synchronous oscillations. However, it may be difficult to create absolutely identical bubbles and, moreover, one can observe in experiments regimes that are unstable with respect to perturbations of equilibrium radii of bubbles. Therefore, we investigate the stability of various synchronous and asynchronous dynamical regimes with respect to the breaking of this symmetry. We show that the main factors determining stability or instability of a synchronous attractor are the presence/absence and the type of an asynchronous attractor coexisting with the synchronous attractor. On the other hand, asynchronous hyperchaotic attractors are stable with respect to the symmetry breaking in all the situations we have studied. Therefore, they are likely to be observed in physically realistic scenarios and can be beneficial for suitable applications when chaotic behavior is desirable.

Actively Mode-Locked Semiconductor Laser with Feedback at an Intermode Frequency

This is a study of an active mode synchronization regime (mode locking) in a three-mirror semiconductor laser obtained by modulation of the laser current at the frequency of intermode beating of the external laser cavity through a feedback circuit. Under certain conditions stable active mode-locking is observed, and when the length of the external cavity is varied, corresponding tuning of the intermode beat frequency occurs. The main conditions under which this regime is attained are determined. The width of the intermode beating spectrum is found experimentally to be ~300 Hz for an intermode frequency of 300 MHz. The half width of the optical spectrum is ~4 nm.

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps.

We study relay and complete synchronization in a heterogeneous triplex network of discrete-time chaotic oscillators. A relay layer and two outer layers, which are not directly coupled but interact via the relay layer, represent rings of nonlocally coupled two-dimensional maps. We consider for the first time the case when the spatiotemporal dynamics of the relay layer is completely different from that of the outer layers. Two different configurations of the triplex network are explored: when the relay layer consists of Lozi maps while the outer layers are given by Henon maps and vice versa. Phase and amplitude chimera states are observed in the uncoupled Henon map ring, while solitary state regimes are typical for the isolated Lozi map ring. We show for the first time relay synchronization of amplitude and phase chimeras, a solitary state chimera, and solitary state regimes in the outer layers. We reveal regimes of complete synchronization for the chimera structures and solitary state modes in all the three layers. We also analyze how the synchronization effects depend on the spatiotemporal dynamics of the relay layer and construct phase diagrams in the parameter plane of inter-layer vs intra-layer coupling strength of the relay layer.

On global mechanisms of synchronization in networks of coupled chaotic circuits and the role of the voltage-type coupling

A model for synchronization of coupled Nakano’s chaotic circuits is studied. The Nakano circuit consists of a simple RLC circuit with a switch voltage-depending reset rule which generates a discontinuous dynamics. Thus, the model that we study is a network of identical spiking oscillators with integrate-and-fire dynamics. The coupling between oscillators is linear, but the network is subject to a common regime of reset depending on the global state of the oscillator population. This constitutes the simplest way of build pulse-coupled networks with arbitrary topology for this type of oscillators, and it allows the emergence of synchronous states and different reset regimes. The main result is that under certain hypothesis over the weight matrix (that represents the network topology) the different reset regimes match and the formalism of the master stability function can be generalized in order to study the stability of the synchronous state and the discontinuous dynamic of the network. Also, the low dimensionality of the Nakano’s circuit allows to implement the saltation-matrix method and numerical simulations can be performed in order to analyze the role of the coupling mode in the synchronization regime of the network and the influence of the voltage-type variables.

Stability of synchronous regimes in unbalanced rotors on elastic base

The stationary dynamics of an unbalanced rotor (vibrator) on a movable base (linear oscillator) under excitation by a driving torque is studied with focusing on the stability of 1:1 stationary regimes of rotation and oscillation. This problem was well studied previously in the first approximation, dealing, in fact, with averaged regimes, mainly in the framework of asymptotic procedures. We use an efficient analytical procedure, proposed in our previous works for another problem, which sequentially separates the averaged regimes and deviations from them. Describing in the first approximation the known features of the synchronous stationary regimes under consideration, this approach in the second approximation results in the analytical solution for nonuniform rotation whose exactness is confirmed in the numerical simulation. The solution enables us to reveal possibility of parametric instability for oscillations of the rotor angular velocity and to describe two possible mechanisms of this instability. It is shown that the known condition of stability of stationary synchronous rotation-oscillation regimes is only necessary but not sufficient criterion, and two additional necessary conditions of stability are obtained and confirmed by the numerical simulation.