Bifurcation Map Research Articles

BOOM: A novel bifurcation stent technique using optical coherence tomography co-registration

Background/purposeBifurcation lesions comprise 20 % of percutaneous coronary interventions (PCI) and are associated with worse long-term outcomes. With an increasing percentage of patients presenting with complex anatomy, including bifurcation disease, there is a need for treatment strategies to optimize PCI outcomes. Methods/materialsWe retrospectively analyzed 48 patients undergoing OCT guided bifurcation PCI using the ‘Bifurcation and Ostial OCT Mapping’ (BOOM) technique. The primary efficacy variable studied was stent precision following deployment, defined as the distance of the most proximal stent strut from the true ostium of the target vessel. Additionally, targeted follow-up occurred by phone at 6- and 12-months post procedure, where the frequency of myocardial infarction, target lesion revascularization, target vessel and non-target vessel revascularization, and mortality were collected. ResultsA total of 40 (83.3 %) had an ostial lesion that required treatment while the remaining patients had true bifurcation disease. Most target lesions were in either the LAD or its branches (29 lesions (60.3 %)). With respect to stent positioning, the median absolute geographic miss, (i.e., stent protrusion into the main branch or lack of complete ostial stent coverage), was 0.75 mm. At 6 months, one patient required target lesion revascularization with no additional patients at 12 months. ConclusionsBOOM is a safe and simple strategy that can be a useful technique to optimize precise stent placement for ostial and bifurcation lesions.

Research on Variable Parameter Color Image Encryption Based on Five-Dimensional Tri-Valued Memristor Chaotic System.

To construct a chaotic system with complex characteristics and to improve the security of image data, a five-dimensional tri-valued memristor chaotic system with high complexity is innovatively constructed. Firstly, a pressure-controlled tri-valued memristor on Liu's pseudo-four-wing chaotic system is introduced. Through analytical methods, such as Lyapunov exponential map, bifurcation map and attractor phase diagram, it is demonstrated that the new system has rich dynamical behaviors with periodic limit rings varying with the coupling parameter of the system, variable airfoil phenomenon as well as transient chaotic phenomenon of chaos-periodic depending on the system parameter and chaos-quasi-periodic depending on the memristor parameter. The system is simulated with dynamic circuits based on Simulink. Secondly, the differently structured synchronous controls of chaotic systems are realized using a nonlinear feedback control method. Finally, based on the newly constructed five-dimensional chaotic system, a variable parameter color image encryption scheme is proposed to iteratively generate varying chaotic pseudo-random sequences by varying the system parameters, which will be used for repetition-free disambiguation, additive modulo left-shift diffusion and DNA encryption for the three components of RGB of the color image after chunking. The simulation results are analyzed by histogram, information entropy, adjacent pixel correlation, etc., and the images are tested using differential attack, noise attack and geometric attack, as well as analyzing the PSNR and SSIM of the decrypted image quality. The results show that the encryption method has a certain degree of security and can be applied to medical, military and financial fields with more complex environmental requirements.

Fractional-Order Modeling and Nonlinear Dynamic Analysis of Forward Converter

To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. And nonlinear dynamical bifurcation maps which use PI controller parameters and a reference current as bifurcation parameters are obtained. The nonlinear dynamic behavior is analyzed and compared with that of an integral-order forward converter. The results show that under certain operating conditions, the fractional-order forward converter exhibits bifurcations characterized by low-frequency oscillations and period-doubling as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the forward converter. The stable zone of the fractional-order forward converter is larger than that of the integral-order one. Therefore, the circuit struggles to enter states of bifurcation and chaos. The stability domain for low-frequency oscillations and period-doubling bifurcations can be accurately predicted by using a small signal model and a predictive correction model of the fractional-order forward converter, respectively. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified.

Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.

Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays

This paper examines a class of two-species reaction-diffusion-advection competition models with two time delays. A system of DDE equations was derived, both theoretically and numerically, using the Galerkin technique method. A condition is defined that helps to find the existence of Hopf bifurcation points. Full diagrams of the Hopf bifurcation points and areas of stability are investigated in detail. Furthermore, we discuss three different sources of delay on bifurcation maps, and what impacts of all these cases of delays on others free rates on the regions of the Hopf bifurcation in this model. We find two different stability regions when the delay time is positive (τ>0), while the no-delay case (τ=0) has only one stable region. Moreover, the effect of delays and diffusion rates on all free others parameters in this model have been considered, which can significantly impact upon the stability regions in both population concentrations. It is also found that, as diffusion increases, the time delay increases. However, as the delay maturation is increased, the Hopf points for both proliferation of the population and advection rates are decreased and it causes raises to the region of instability. In addition, bifurcation diagrams are drawn to display chosen instances of the periodic oscillation and two dimensional phase portraits for both concentrations have been plotted to corroborate all analytical outputs that investigated in the theoretical part.

Application of two-dimensional chaotic system and implementation of DSP

Abstract Given that the limited complexity of most current 2D maps undermines chaos-based practical applications, this paper proposes a 2D Logical Cosine Coupled Map (2D-LSCCM) and compares the bifurcation maps, Lyapunov exponent spectrum, and spectral entropy complexity of the classical 2D chaos model. Based on this model, this paper proposes an image encryption scheme using ascending alignment permutation and XOR pixel diffusion algorithm. After a series of tests, such as chi-square test, anti-attack test, key sensitivity test, and correlation test, the simulation findings show that the chaotic system proposed in this paper has excellent security performance compared with other systems. Moreover, a hardware platform based on DSP (Digital Signal Processing) and NIST test have been developed to analyze and test chaotic sequences.

Multi-Parameter Practical Stability Region Analysis of Wind Power System Based on Limit Cycle Amplitude Tracing

The existing division of system stability region does not fully consider the influence of nonlinear characteristics of the system. To address the challenge that it is difficult to inscribe the stability region of wind power grid-connected systems accurately and quantitatively, this paper proposes a nonlinear system multi-parameter practical stability region analysis method based on limit cycle amplitude tracking. Firstly, the nonlinear dynamic model of multi-machine system with doubly fed induction generator (DFIG) is established, and the bifurcation diagram of the system is obtained by nonlinear analysis of the model. Then, the limit cycle-parameter diagram is obtained by tracking the limit cycle of the Hopf bifurcation point of the system, and the problem of how the system oscillation evolves with the change of operating parameters is analyzed. Afterwards, the single parameter practical stability region of the nonlinear system is obtained by combining the system equilibrium manifold. Finally, the multi-parameter practical stability region of the nonlinear system is obtained by the three-dimensional bifurcation map with the system time delay, DFIG output active power and reactive load as the bifurcation parameters. The division of the stability region has important guiding significance for the parameter adjustment in the actual operation of the system.

Bifurcation analysis of a wheel‐slip control loop under low wheel‐slip regulation considering time‐delay

AbstractSafety and efficiency are key aspects of research and development in the automotive industry, especially in the field of safety‐critical subsystems, such as brake systems. The effect of time delay arise in brake systems, this adverse effect can cause performance degradations or make the brake system unstable. In this study, the bifurcation analysis of a wheel slip control feedback loop is presented. The control system consists of a wheel and a tyre, delayed actuator dynamics, and an LQR (linear quadratic regulator) that is designed to operate under relatively low wheel slip, during service braking. As a result, it is shown, that if time delay is neglected, the steady‐state solution of the model is globally stable using the LQ optimal controller gains. However, considering nonzero time‐delay may cause a subcritical Hopf‐bifurcation, and an unstable limit‐cycle exists around the steady‐state solution in a large domain of time‐delay parameters. Critical bifurcation maps and simulation results with more detailed system models are generated and shown in the study.

Investigating the Effects of a Fractional Operator on the Evolution of the ENSO Model: Bifurcations, Stability and Numerical Analysis

Recent years have seen an increase in scientific interest in the El Nio/La Nia Southern Oscillation (ENSO), a quasiperiodic climate phenomenon that takes place throughout the tropical Pacific Ocean over five years and causes significant harm. It is associated with the warm oceanic stage known as El Nio and the cold oceanic stage known as La Nia. In this research, the ENSO model is considered under a fractional operator, which is defined via a nonsingular and nonlocal kernel. Some theoretical features, such as equilibrium points and their stability, bifurcation maps, the existence of a unique solution via the Picard–Lindelof approach, and the stability of the solution via the Ulam–Hyres stability approach, are deliberated for the proposed ENSO model. The Adams–Bashforth numerical method, associated with Lagrangian interpolation, is used to obtain a numerical solution for the considered ENSO model. The complex dynamics of the ENSO model are displayed for a few fractional orders via MATLAB-18.

Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes

For a system encompassing subsystems, dynamic modal interaction may experience unanticipated vibrations among subsystems that are excited indirectly. This paper focuses attention to a nonlinear auto-parametric resonance phenomenon of a flexible beam introduced via modal coupling of longitudinal forced resonance and transverse parametric resonance under longitudinal pulsatile excitation. The coupled resonance equations are first modeled based on the Euler-Bernoulli beam theory by incorporating nonlinear curvature, von Kármán's nonlinear strain-displacement relationship and the flexible beam model characterizing nonlinear inertia and displacement interaction. The Galerkin truncation-incremental harmonic balance method (IHBM) is then introduced to obtain both the stability boundary and amplitude-frequency bifurcation maps. Through the corresponding relationship between stability boundary and bifurcation diagram, the energy exchange between two modes is identified as well as the instability region and bifurcation topology can be tuned. It is found that the modal interaction greatly widens the instability region with at most two resonance bands of lateral resonance. By tuning structural and foundation damping, resonance can be controlled to occur only in one frequency band of the pair as desired. This research provides guidance to design broadband energy harvesting or vibration suppression equipment with tunable working frequency band for using the strategy of auto-parametric resonance.

Community analysis of bifurcation maps of diluted hydrogen combustion in well stirred reactors

This article focuses on applying an automatic procedure for inspecting detailed kinetic mechanisms to predict key species/reactions playing a dominant role in the dynamic behaviour of regime transitions of combustion systems. We adopted a novel analysis method of kinetic mechanisms built by coupling the bifurcation analysis, which identifies the different regimes occurring with a change of the parameters, with algorithms typical of Artificial Intelligence, specifically the Community Analysis, which identifies within a large set of individuals (the chemical species) common behaviour patterns. Then we showed that this method is capable of automatically extracting meaningful information to identify the key species responsible for the dynamic behaviour and change of regimes observed in the solution maps of a combustion system. Application to a diluted hydrogen combustion system is illustrated as a first validation bench. It reveals that the recognition of state change is effective when based on proper indexes. On the full range of the parameter investigated, the inlet mixture temperature, when adopting an index correlated to the heat release rate, different community partitions were identified for each of the three regions with different dynamic behaviour. The most complex community partitions, with three communities, arise in the first two regions of lower temperature. The partition simplifies in the region of the higher parameter values where the system shows steady solutions without oscillations. The change in the link of atomic hydrogen, OH, and H2O2 with the remaining species is identified in the regime transitions.

Harnessing adaptive bistable stiffness of hair-cell-bundle structure for broadband vibration applications

This study presents an initial study on the adaptive bistable stiffness of the hair cell bundle structure in a frog cochlea, and aims to harness its bistable nonlinearity that features a negative stiffness region for broadband vibration applications such as vibration-based energy harvesters. To this end, the mathematical model for describing the bistable stiffness is first formulated based on the modeling concept of piecewise type nonlinearities. The harmonic balance method was then employed to examine the nonlinear responses of bistable oscillator, mimicking hair cells bundle structure under the frequency sweeping condition, and their dynamic behaviors induced by bistable stiffness characteristics are projected on phase diagrams, and Poincare maps concerning the bifurcation. In particular, the bifurcation mapping at the super- and sub-harmonic regimes provides a better perspective to examine the nonlinear motions which occur in the biomimetic system. The use of bistable stiffness characteristics of hair cell bundle structure in frog cochlea thus offers physical insights to harness the adaptive bistable stiffness for metamaterial-like potential engineering structures such as vibration-based energy harvester, and isolator etc.

Effect of internal excitation induced by non-uniform contact of roller bearings on nonlinear vibration and stability of rotor system under combined loads

The misalignment of roller bearing rings will results in moment load, together with the unbalance and external loads, forming the combined dynamic loads. The complex combined load can cause non-uniform contact of rollers and rings, which reduces the bearing’s life and significantly affect the vibration of rotor systems. This paper mainly studies the roller bearing internal contact performances under combined loads and the influence of internal excitation on the nonlinear vibration of rotor systems. First, the “slices” method is used to establish the mechanical model of roller bearings, which considers the radial clearance and nonlinear Hertz contact. The obtained time-varying bearing nonlinear support reaction is introduced into the rotor concentrated mass model, and a roller bearing–rotor system dynamic model is proposed. Further, the system’s complex nonlinear vibrations, such as bifurcation and chaos, are analyzed by spectrum, orbits, bifurcation, and Poincare map. The roller bearing contact performances and stability under the influence of ring tilt angle, rotational speed, and unbalance, are analyzed by contact load statistical features. Finally, based on a rolling bearing–rotor test rig, the vibration experiment considering the combined load was performed, and the experiment results are compared with simulation results to verify the proposed model and conclusions.

OPTIMIZATION OF RISERBASE GAS INJECTION FOR SLUG FLOW ATTENUATION

A new approach for the optimization of riserbase gas injection for slug flow attenuation has been proposed. Riserbase gas injection is an established method for slug flow mitigation, however it can be expensive due to the high volume of gas required and the cost of compression. In this study, optimum gas volumes required to stabilise a range of unstable slug flow conditions were obtained using bifurcation maps. The results showed that at the bifurcation point, minimum gas injection volume is required to achieve flow stability. This study established that the optimum gas volume required is dependent on the type of slug flow. For a very high frequency slug flow at high flow rate more volume of gas up to 100kg/s is required to achieve stability while slug flow at moderate flow rate could need up to 30kg/s and slug at low flow rate required about 6 kg/s to achieve stability. The developed approach in this work can help reduce the overall cost of gas injection for slug flow mitigation. Keywords: Slug attenuation; Bifurcation; Gas injection; slug flow; multiphase flow.

Surface instabilities of soft dielectric elastomers with implementation of electrode stiffness

This paper contains a thorough investigation into plane-strain electroelastic surface instabilities of dielectric elastomers. We employ a systematic approach to our investigation, introducing three ways to actuate an elastomer device, namely, actuation by means of (1) attached compliant electrodes, (2) sprayed charges onto the opposite surfaces, and (3) fixed electrodes between which the device “floats” in vacuum and expands transversally. We examine electromechanical instability with particular attention to the third listed mode of actuation and the features of the specimen. We then tackle surface instability for the three modes, showing the relationship between applied pre-stress and the stability domain, as well as the characteristics of the obtained bifurcation fields. The effects of the stiffness of the electrode (relevant in the first listed mode of actuation) on surface instabilities are then investigated by adopting an elastic surface–substrate interaction model in which the properties of the coating enter the boundary conditions for the substrate. Various electrode materials are assumed, demonstrating that their implementation in the model increases the number of solutions at bifurcation and changes the overall stability domain. We present this new enriched bifurcation map, showing the dependence on the wavenumber, and characterise the solutions by examining the bifurcated fields.

Community Analysis of Bifurcation Maps of Diluted Hydrogen Combustion in WSRs

Community Analysis of Bifurcation Maps of Diluted Hydrogen Combustion in WSRs

Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay

This paper considers both analytical and numerical solutions for a diffusive Schnakenberg model with gene-expression time delays, presenting an analysis of the effects of delays and diffusion on stability regions and bifurcation maps. A one-domain system was considered. Systems of delay ODEs were obtained using the Galerkin method. Theoretical conditions for the existence of steady-state and Hopf bifurcation curves were determined. In addition, Hopf bifurcation points and bifurcation stability regions were plotted in detail. The gene-expression time delays and diffusion rates influenced the stability regions for both reactant concentration controls in the system. The results showed that, with increases in time delays, the rates of the Hopf bifurcation points for both chemical concentrations controls decreased, while both parameters of the diffusion coefficient grew as the chemical control values increased. Numerical simulations for bifurcation diagrams, limit cycles, and periodic routes to chaotic behaviour planes confirm the solutions achieved from theory.

Effect of the wavy geometric disturbance on the flow over elliptic cylinders with different aspect ratios

The present study investigates the effect of the wavy geometric disturbance as the flow control on the flow around elliptic cylinders with different aspect ratios at low Reynolds number of 100. The wide ranges of the wavelength (1.0≤λ/Lm,x≤8.0) and the aspect ratio of the ellipse (0.5≤AR≤1.0) are considered, where Lm,x is the streamwise mean body length. For AR=1.0 with the circular cross-section, the flow strongly depends on λ/Lm,x, resulting in the appearance of various flow structures. As AR decreases, the flow bifurcation occurs at the certain conditions of AR and λ/Lm,x. Therefore, the bifurcation map is presented in AR−λ/Lm,x plane, where flows are classified as three modes of the unsteady, steady and coexistence states. There are two effects of the waviness and the streamlined body on the flow bifurcation. At the large ARs in AR>0.6, the bifurcation early occurs from the long wavelengths, which is associated to two types of the streamwise vorticities. In AR≤0.6, the effect of the streamlined body on the flow overcomes the wavy geometric disturbance, resulting in undergoing the bifurcation, regardless of λ/Lm,x. Additionally, force coefficients and the Strouhal number are analyzed to understand the dependence of hydrodynamic performance and vortex shedding on AR and λ/Lm,x.

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

Predicting the domain and nature of instabilities in charging and discharging Li batteries

A pattern of sequential group-by-group charging or discharging, of Li batteries with phase-separation thermodynamics, was detected by numerical simulations and justified by several experiments published in literature. The present work is the first to quantitatively predict the main characteristics of the sequential symmetry breaking (SB) events, such as the average Li concentration and the fraction of the Li-poor part at the SB transition times. Using a reduced two-zone (Li-poor and Li-rich) model, that ignores gradients in the liquid phase potential (ϕl), we derive an approximate solution predicting the effect of non-uniformity in initial conditions or in imposedparameter (collectively referred to as 'noise') on the characteristics. We show that gradients in ϕl, although extremely small, operate like noise leading to break-up of the homogeneous solution. A bifurcation map, showing the lowest current boundary that ensures a homogeneous lithiation/ delithiation as a function of noise level, is constructed.