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.     

双馈风力发电机混沌运动分析及滑模控制混沌同步

以双馈风力发电机组(DFIG)为研究对象,推导了其dq轴数学模型. 根据某2MW主流双馈电机实际参数,论证了在某些参数及工作条件下会出现混沌运动. 基于主动控制思想,设计了一种主动滑模控制器,使得从任意初始条件出发均能保证系统稳定. 基于Lyapunov稳定性理论分析了系统稳定性. 以双馈电机模型为例进行数值仿真验证,较快的实现了混沌系统同步. 仿真结果表明该控制方法具有良好的鲁棒性和稳定性. 关键词： 风力发电 双馈风力发电机组(DFIG) 混沌控制和滑模控制 同步     

激光时空混沌模型的加权网络投影同步

提出了一种实现加权网络时空混沌投影同步的方法.通过构造合适的Lyapunov函数,确定了加权网络中连接节点之间耦合函数的结构以及网络节点状态方程中分离配置的线性项的系数矩阵的取值范围.以Bragg声光双稳系统作为局域函数,单向耦合映像格子作为空间扩展系统构成激光时空混沌模型.通过仿真模拟检验了采用激光时空混沌模型作为网络节点的加权网络的投影同步效果.结果显示,对于任意的节点之间耦合强度的权重值,加权网络的投影同步均可以实现. 关键词： 投影同步 加权网络 时空混沌 Bragg声光双稳系统     

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.     

心脏中的螺旋波和时空混沌的抑制研究

以Luo-Rudy相I心脏模型为基础,研究心脏中螺旋波和时空混沌的控制,提出了两种控制方法: (Ⅰ)通过交替改变细胞外钾离子浓度来产生平面波,再利用弱外电场辅助平面波抑制螺旋波和时空混沌; (Ⅱ)先提高细胞外钾离子浓度,然后利用外电场激发波的方式产生平面波,再用平面波去抑制螺旋波和时空混沌. 研究结果表明,只要适当选择控制参数,这两种方法都能够有效抑制螺旋波和时空混沌. 当心肌出现局部缺血时,在心肌缺血处就会出现高的细胞外钾离子浓度,在这种情况下, 可以采用电场发射波的方法来抑制心脏中的螺旋波和时空混沌.对这些控制方法的优点和控制机制做了解释.     

广义混沌同步中的多稳定同步流形

从构造驱动系统和响应系统之间的函数关系出发,一般性地研究了广义混沌同步中同步流形的多值性问题,并对同步流形的稳定性进行了分析,提出了多稳定同步流形存在的条件.利用该稳定性条件对两个实例进行了分析,一个为Genesio-Rssler耦合系统,另一个为具有二次、三次非线性的耦合Duffing系统,结果表明前者仅有唯一的稳定同步流形,而后者随着耦合强度的增加,从具有两个稳定的同步流形变为只存在一个稳定同步流形. 关键词： 混沌同步 多稳定性 同步流形     

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.     

局域反馈抑制心脏中的螺旋波和时空混沌

采用LuoRud91模型研究了螺旋波和时空混沌的抑制,提出用局域反馈控制方法抑制螺旋波和时空混沌,采用静止和运动控制器两种控制策略.结果表明:适当选择控制参数,静止控制器的局域反馈方法能很好抑制螺旋波,但不能有效抑制时空混沌;采用运动控制器的局域反馈方法能有效抑制螺旋波和时空混沌,抑制速度与控制器移动的速度有关,在选择适当的控制参数下,螺旋波和时空混沌能在很短的时间内被抑制.     

Projective synchronization of spatiotemporal chaos in a weighted complex network

<正>Projective synchronization of a weighted complex network is studied in which nodes are spatiotemporal chaos systems and all nodes are coupled not with the nonlinear terms of the system but through a weighted connection.The range of the linear coefficient matrix of separated configuration,when the synchronization is implemented,is determined according to Lyapunov stability theory.It is found that projective synchronization can be realized for unidirectional star-connection even if the coupling strength between the nodes is a given arbitrary weight value.The Gray-Scott models having spatiotemporal chaos behaviours are taken as nodes in the weighted complex network,and simulation results of spatiotemporal synchronization show the effectiveness of the method.     

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．     

一个简单延迟非线性系统的动力学行为及混沌同步

分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果. 关键词： 延迟非线性系统 电路实验 Hopf分支 混沌     

简并光学参量振荡器混沌相同步与反相同步

从广泛意义上研究了简并光学参量振荡器的混沌同步. 数值结果表明, 当最大条件李指数小于零时, 处于混沌态的两个简并光学参量振荡器通过单向耦合可以实现相同步或反相同步. 当两个简并光学参量振荡器同时实现正耦合或负耦合时为相同步, 当其中一个为正耦合而另一个为负耦合时实现反相同步.     

Generalized synchronization of chaos in erbium—doped dual—ring lasers

We investigate chaotic synchronization in the generalized sense in unidirectionally coupled erbium-doped fibre dual-ring lasers. Numerical simulation shows that no matter whether the two different erbium-doped fibre dual-ring lasers are chaotic or not before coupling, they show generalized synchronization with a suitable unidirectional coupling coefficient under which the maximum condition Lyapunov exponent is negative. We also use the auxiliary system approach to detect the generalized synchronization.     

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.