From local to global spatiotemporal chaos in a cardiac tissue model

Two kinds of chaos can occur in cardiac tissue, chaotic meander of a single intact spiral wave and chaotic spiral wave breakup. We studied these behaviors in a model of two-dimensional cardiac tissue based on the Luo-Rudy I action potential model. In the chaotic meander regime, chaos is spatially localized to the core of the spiral wave. When persistent spiral wave breakup occurs, there is a transition from local to global spatiotemporal chaos.     

Alternans amplification following a two-stimulus protocol in a one-dimensional cardiac ionic model of reentry: from annihilation to double-wave quasiperiodic reentry

Electrical pacing is a common procedure in both experimental and clinical settings to study and/or annihilate anatomical reentry. A previous study [Comtois and Vinet, Chaos 12, 903 (2002)] has described new ways to terminate reentry in a one-dimensional loop model by a protocol consisting of only two stimulations. Annihilation of the reentrant activity was much more likely with these new scenarios than through a unidirectional block. This paper investigates the sensitivity of these scenarios of annihilation to the length of the pathway. It shows that double-pulse stimulation can stop the reentry if the circuit is shorter than a limiting length. Beyond this upper limit, stimulation rather yields sustained double-wave reentry. The same dynamical mechanism, labeled alternans amplification, is found to be responsible for these two types of post-stimulus dynamics.     

The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential

This review examines the initiation of reentry in cardiac muscle by strong electric shocks. Specifically, it concentrates on the mechanisms by which electric shocks change the transmembrane potential of the cardiac membrane and create the physiological substrate required by the critical point theory for the initiation of rotors. The mechanisms examined include (1) direct polarization of the tissue by the stimulating current, as described by the one-dimensional cable model and its two- and three-dimensional extensions, (2) the presence of virtual anodes and cathodes, as described by the bidomain model with unequal anisotropy ratios of the intra- and extracellular spaces, (3) polarization of the tissue due to changing orientation of cardiac fibers, and (4) polarization of individual cells or groups of cells by the electric field ("sawtooth potential"). The importance of these mechanisms in the initiation of reentry is examined in two case studies: the induction of rotors using successive stimulation with a unipolar electrode, and the induction of rotors using cross-field stimulation. These cases reveal that the mechanism by which a unipolar stimulation induces arrhythmias can be explained in the framework of the bidomain model with unequal anisotropy ratios. In contrast, none of the examined mechanisms provide an adequate explanation for the induction of rotors by cross-field stimulation. Hence, this study emphasizes the need for further experimental and theoretical work directed toward explaining the mechanism of field stimulation. (c) 1998 American Institute of Physics.     

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.     

Dual synchronization of chaos in microchip lasers

We have achieved dual synchronization of chaos in two pairs of one-way coupled Nd:YVO4 microchip lasers, using only one transmission channel, by experiment and numerical calculation. We observed the individual synchronization of chaos in each pair of two lasers by adjusting the optical frequencies for injection locking between the corresponding pairs. The achievement of dual synchronization is dependent on the injection-locking condition, which is different from the locking condition for a single pair of lasers because of the presence of an additional injection signal from the master laser of the other pair.     

Symmetry breaking,bifurcations, quasiperiodicity,and chaos due to electric fields in a coupled cell model

A model for the asymmetric coupling of two oscillatory cells is considered. The coupling between the cells is both through diffusional exchange (symmetric) and through the electromigration of ionic reactant species from one cell to the other (asymmetric) in applied electric fields. The kinetics in each cell are the same and based on the Gray-Scott scheme. Without the electric field, only simple, stable dynamics are seen. The effect of the asymmetry (applying electric fields) is to create a wide variety of stable dynamics, multistability, multiperiodic oscillations, quasiperiodicity and chaos being observed, this complexity in response being more prevalent at weaker coupling rates and at weaker field strengths. The results are obtained using a standard dynamical systems continuation program, though asymptotic results are obtained for strong coupling rates and strong electric fields. These are seen to agree well with the numerically determined values in the appropriate parameter regimes. (c) 2002 American Institute of Physics.     

在大学物理教学中适当增加混沌控制和同步内容的重要性

阐述了在大学物理教学中引入非线性理论知识,特别是引入混沌控制和同步内容的重要性,这对于让学生完整理解混沌科学理论是非常必要的．     

Designing coupling for synchronization and amplification of chaos

We propose a design of coupling for stable synchronization and antisynchronization in chaotic systems under parameter mismatch. The antisynchronization is independent of the specific symmetry (reflection symmetry, axial symmetry, or other) of a dynamical system. In the synchronization regimes, we achieve amplification (attenuation) of a chaotic driver in a response oscillator. Numerical examples of a Lorenz system, R?ssler oscillator, and Sprott system are presented. Experimental evidence is shown using an electronic version of the Sprott system.     

Investigation of chaos synchronization in photonic crystal lasers

Chaotic dynamics and chaos synchronization in photonic crystal (PC) lasers with optical feedback are investigated numerically. The effect of various system parameters such as amplitude reflectivity of the external mirror “r”, external cavity length “L_e”, and injection current “I” on system dynamics is addressed in detail. Simulation results are presented using MATLAB to address system behavior. The parameters r, L_e, and I are varied over the ranges (0.05–0.25), (2.8–3.2 mm), and (1.1I_th–2I_th), respectively. The results indicate that very small parameter mismatches between the transmitter laser and receiver laser affect strongly complete chaos synchronization between them.     

Experimental observation of nonlinear synchronization due to a single wave

A test electron beam is propagated in a specially designed traveling wave tube. It interacts with a nonresonant wave, and its energy distribution is recorded at the tube output. We report the direct experimental observation of the spatially periodic electron velocity bunching, and of a nonlinear effect on the electron velocity modulation: the synchronization of the particles with the wave responsible for Landau damping in plasma physics. The results are explained by second order perturbation theory in the wave amplitude.     

Chaos synchronization in RCL-shunted Josephson junctions via a common chaos driving

We study chaos synchronization in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using a common chaos driving. The numerical simulations confirm that the synchronization of two RCLSJJs can be achieved with a suitable driving intensity when the maximum condition Lyapunov exponent (MCLE) is negative.     

Homoclinic chaos in a laser: synchronization and its implications in biological systems

Phase synchronization of a CO₂ laser with feedback, exhibiting homoclinic chaos, is realized by a tiny periodic perturbation of a control parameter. The deviations of the modulation frequency from the optimal one induce phase slips, thus yielding an imperfect phase synchronization. Based on the information of these phase slips, the modulation frequency can be readjusted until the phase slips are eliminated. In this way, a control loop which detects the phase slips provides an adaptive tracking of the natural frequency of the dynamical system. Moreover, we have shown that the system's susceptibility is largest when a periodic impulsive perturbation is applied near the saddle focus.     

Collective chaos synchronization of pairs of modes in a chaotic three-mode laser

We study chaos synchronization experimentally in a modulated globally coupled three-mode laser with different modal gains subjected to self-mixing Doppler-shifted feedback, which can apply the loss modulation to individual modes at Doppler-shift frequencies. Depending on the pump power, different forms of collective chaos synchronizations were found to appear when the laser was modulated at the highest relaxation oscillation frequency, reflecting the change in cross-saturation coefficient among modes. In the present experiment, each pair of modes exhibited phase, lag, or generalized synchronization collectively according to the inherent antiphase dynamics, where these types of synchronization have already been demonstrated in two coupled chaotic oscillators in different physical systems. Information flows among oscillating modes which are established in different forms of collective chaos synchronizations were characterized by information-circulation analysis of the experimental time series. (c) 2002 American Institute of Physics.     

Generalized synchronization of spatiotemporal chaos in a liquid crystal spatial light modulator

We demonstrate generalized synchronization in a spatiotemporal chaotic system, a liquid crystal spatial light modulator with optoelectronic feedback.     

Spatio-temporal chaos in a chemotaxis model

In this paper we explore the dynamics of a one-dimensional Keller–Segel type model for chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the model to self-organise into multiple cellular aggregations which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coalesce) and emerging (a new aggregation appears). This spatio-temporal patterning can be further subdivided into either a time-periodic or time-irregular fashion. Numerical explorations into the latter indicate a positive Lyapunov exponent (sensitive dependence to initial conditions) together with a rich bifurcation structure. In particular, we find stationary patterns that bifurcate onto a path of periodic patterns which, prior to the onset of spatio-temporal irregularity, undergo a “periodic-doubling” sequence. Based on these results and comparisons with other systems, we argue that the spatio-temporal irregularity observed here describes a form of spatio-temporal chaos. We discuss briefly our results in the context of previous applications of chemotaxis models, including tumour invasion, embryonic development and ecology.     

Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree

The paper presents a study of synchronization phenomena in a system of 22 nephrons supplied with blood from a common cortical radial artery. The nephrons are assumed to interact via hemodynamic and vascularly propagated coupling, both mediated by vascular connections. Using anatomic and physiological criteria, the nephrons are divided into groups: cortical nephrons and medullary nephrons with short, intermediate and long Henle loops. Within each of these groups the delay parameters of the internal feedback regulation are given a random component to represent the internephron variability. For parameters that generate simple limit cycle dynamics in the pressure and flow regulation of single nephrons, the ensemble of coupled nephrons showed steady state, quasiperiodic or chaotic dynamics, depending on the interaction strengths and the arterial blood pressure. When the solutions were either quasiperiodic or chaotic, cortical nephrons synchronized to a single frequency, but the longer medullary nephrons formed two clusters with different frequencies. Under no physiologically realistic combination of parameters did all nephrons assume a common frequency. Our results suggest a greater variability in the nephron dynamics than is apparent from measurements performed on cortical nephrons only. This variability may explain the development of chaotic dynamics in tubular pressure records from hypertensive rats.     

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.