Evolution of Spiral Waves under Modulated Electric Fields

Spirals generated from the excitable media within the Barkley model is investigated under the gradient electric fields by a numerical simulation. The spiral drift and spiral break up are observed when the amplitude of the electric fields is modulated by a constant signal or a chaotic signal. It is also verified that, even in the presence of the white noise, the whole system can reach homogeneous states after the spiral breakup, by using an adaptive strategy.     

时变反应扩散系统中螺旋波和湍流的控制

研究了一类参数时变的反应扩散系统中螺旋波和湍流对外电场的响应问题.在数值模拟中,以一类改进的Fitzhugh-Nagumo模型为研究对象(在恰当参数值下可分别描述激发介质和振荡介质),考虑随机和不确定因素(如内外噪声、气压、温度梯度分布和介质形变等)所引起的系统参数涨落对斑图演化的影响,在模拟中选取的参数涨落范围确保系统可以观测到稳定旋转的螺旋波、漫游的螺旋波和湍流,经历一定的暂态过程后,对介质施加极化电场,研究螺旋波和湍流在外电场中的演化.数值计算结果表明：在系统参数发生涨落和外电场强度比较小情况下,主 关键词： 螺旋波 湍流 时变系统 Fitzhugh-Nagumo模型     

Electromagnetic wave chaos in gradient refractive index optical cavities.

Electromagnetic wave chaos is investigated using two-dimensional optical cavities formed in a cylindrical gradient refractive index lens with reflective surfaces. When the planar ends of the lens are cut at an angle to its axis, the geometrical ray paths are chaotic. In this regime, the electromagnetic mode spectrum of the cavity is modulated by both real and ghost periodic ray paths, which also "scar" the electric field intensity distributions of many modes. When the cavity is coupled to waveguides, the eigenmodes generate complex series of resonant peaks in the electromagnetic transmission spectrum.     

Sharp diffraction peaks from chaotic structures

Recently various models for spatially chaotic structures have been proposed. We study the diffraction patterns produced by plane chaotic waves incident on one-dimensional chaotic point scatterers. The spacing between the scatterers and the dynamics of the incident wave are given by a logistic map or standard map. We find a sharp diffraction peak when the incident dynamics is produced by the same map as the structure of the spatial configuration. The diffraction pattern is symmetric about the incident direction only if the map dynamics is invertible. Diffraction patterns with chaotic incident waves have a large signal-to-noise ratio and are well suited for pattern identification. We discuss possible applications to the scattering of microwaves from aperiodic structures. (c) 1997 American Institute of Physics.     

Period matching in modulated maps

We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.     

用离散混沌信号驱动实现混沌同步

提出了用离散混沌系统驱动连续混沌系统导致其同步的方法,以逻辑映象、Henon映象、Lorenz系统为例,数值地研究了这种混沌同步方法.模拟结果表明,当驱动信号的强度足够大时,可使两个连续混沌系统达到完全同步,且输出信号具有类似于白噪声的宽谱特性.同时研究了用该混沌同步方法实现保密通信的可能性. 关键词：     

一种新的分段非线性混沌映射及其性能分析

结合线性反馈移位寄存器（LFSR）和混沌理论各自的优点,采用循环迭代结构,给出一种将LFSR和混沌理论相结合的伪随机序列生成方法.首先根据LFSR的计算结果产生相应的选择函数,通过选择函数确定当前迭代计算使用的混沌系统,应用选择的混沌系统进行迭代计算产生相应的混沌序列;然后把生成的混沌序列进行数制转换,在将得到的二进制序列作为产生的伪随机序列输出的同时将其作为反馈值与LFSR的反馈值进行相应的运算,运算结果作为LFSR的最终反馈值,实现对LFSR生成序列的随机扰动.该方法既可生成二值伪随机序列,也可生成实值伪随机序列.通过实验对生成的伪随机序列进行了分析,结果表明,产生的序列具有良好的随机性和安全性.     

一种新的分段非线性混沌映射及其性能分析

研究了logistic混沌映射的相关性质,指出当系统参数取值改变时,产生的混沌序列在相空间不具有遍历性.基于以上分析,构造了一种分段logistic混沌映射,对logistic映射和定义的分段logistic映射的分岔图和Lyapunov指数进行了研究,同时通过实验对这二种映射生成序列的随机性、相关系数、功率谱等性能进行了比较分析.在此基础上,定义了一种新的混沌系统性能评价指标——分岔迭代次数.结果表明,定义的分段logistic映射不仅具有良好的遍历性,而且对应的混沌系统相关评价指标的性能良好. 关键词： 混沌系统 相关系数 Lyapunov指数 功率谱     

Bifurcation structure and Lyapunov exponents of a modulated logistic map

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.     

Spiral Wave in Small-World Networks of Hodgkin--Huxley Neurons

The effect of small-world connection and noise on the formation and transitionof spiral wave in the networks of Hodgkin-Huxley neurons are investigated in detail. Some interesting results are found in our numerical studies. i) The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii) A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise. iii) Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv) Gaussian white noise is introduced on the membrane of neuronsto study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Gaussian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.     

极化电场对可激发介质中螺旋波的控制

螺旋波在不同的物理、化学和生物系统中普遍存在.周期外场,比如极化电场,尤其是具有旋转对称性的圆极化电场可对螺旋波动力学产生重要影响.本文综述了极化电场对可激发介质中螺旋波的控制,包括共振漂移、同步、手征对称性破缺、多臂螺旋波的稳定、次激发介质中的螺旋波、三维回卷波湍流态的控制、心脏组织中螺旋波的去钉扎、心脏组织中螺旋波湍流态的控制等.     

分布式电流刺激抑制心肌组织中螺旋波

利用两种恒定电信号刺激介质不同区域来产生分布式电流, 外界分布式电流内化为跨膜电流后在介质中形成稳定的梯度力可抑制螺旋波的传播. 当螺旋波被消除后系统进一步演化为均匀态且对应的膜片电位采样序列逐渐趋于一个稳定值. 在考虑噪声情况下, 该方法仍然能消除螺旋波, 对其采样序列分析也验证了方法的可靠性. 关键词： 螺旋波 分布式电流 激发介质     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

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.     

Synchronization based system identification of an extended excitable system

A basic state and parameter estimation scheme for an extended excitable system is presented, where time series from a spatial grid of sampling points are used to drive and synchronize corresponding model equations. Model parameters are estimated by minimizing the synchronization error. This estimation scheme is demonstrated using data from generic models of excitable media exhibiting spiral wave dynamics and chaotic spiral break-up that are implemented on a graphics processing unit.     

New communication schemes based on adaptive synchronization

In this paper, adaptive synchronization with unknown parameters is discussed for a unified chaotic system by using the Lyapunov method and the adaptive control approach. Some communication schemes, including chaotic masking, chaotic modulation, and chaotic shift key strategies, are then proposed based on the modified adaptive method. The transmitted signal is masked by chaotic signal or modulated into the system, which effectively blurs the constructed return map and can resist this return map attack. The driving system with unknown parameters and functions is almost completely unknown to the attackers, so it is more secure to apply this method into the communication. Finally, some simulation examples based on the proposed communication schemes and some cryptanalysis works are also given to verify the theoretical analysis in this paper.     

一种基于强跟踪滤波的混沌保密通信方法

提出了一种基于强跟踪滤波器的混沌保密通信方法. 在发送端, 混沌映射和信息符号被建模成非线性状态空间模型, 信息符号被加性混沌掩盖或乘性混沌掩盖调制, 然后通过信道输出. 在接收端, 驱动信号被接收, 使用带有贝叶斯分类器(信息符号估计)的强跟踪滤波器算法动态地恢复信息符号. Logistic混沌映射的仿真表明, 当信息符号为二进制编码时, 不管是加性混沌掩盖调制还是乘性混沌掩盖调制, 强跟踪滤波器均能较好地从混沌信号中恢复信息符号. 与扩展卡尔曼滤波器相比, 由于卡尔曼滤波器对于离散的信息符号跟踪能力差, 混沌映射中信息符号难以恢复, 比特误码率高. 因此, 这种基于强跟踪滤波器的混沌保密通信方法是有效的.     

Evolution of spiral wave and pattern formation in a vortical polarized electric field

In this paper, the evolution of the pattern transition induced by the vortical electric field （VEF） is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.     

非连续反馈控制激发介质中的螺旋波

采用非连续反馈方法来控制Fitz-Hugh-Nagumo方程描述的激发介质中的螺旋波. 在控制过程中,对于系统各个格点快变量的幅值进行观测并和设定的阈值进行比较,当采样格点的快变量的值大于这个阈值时,则对系统进行直接小幅度的负反馈. 研究发现：在对系统所有格点快变量幅值观测时选择比较小的阈值则更容易将系统的螺旋波消除掉并使系统达到稳定均匀态. 在比较大的阈值下,系统的螺旋波则变得稀疏,也可以导致螺旋波的破裂. 在任意选择单个格点的快变量观测下,比较小的反馈强度仍然可以消除螺旋波,系统也达到稳定均匀态. 当 关键词： 螺旋波 Fitz-Hugh-Nagumo方程 反馈控制     

Electric field effect on refraction of light in a layer of chiral liquid crystal with large pitch

The effect of an alternating electric field on the trajectory of an extraordinary light wave in a layer of a chiral liquid crystal with a 180° turn of the director is studied. In this structure, in the absence of the field and at a large angle of incidence of the light wave on the liquid crystal layer, the light undergoes refraction inside the layer. It is shown that the deformation of the director that arises under the action of the electric field changes the character of refraction of the extraordinary wave and the layer begins to transmit the light. The threshold voltage of this effect is determined. The dynamics of the effect is studied. At large voltages, in addition to the extraordinary wave, an ordinary light wave is observed in the light passed through the cell. The ordinary wave intensity is modulated by the initial frequency of the control signal, whereas the extraordinary wave intensity is modulated by the double initial frequency.