Synchronizing spiral waves in a coupled Rssler system

The synchronisation of spiral patterns in a drive-response Rssler system is studied.The existence of three types of synchronisation is revealed by inspecting the coupling parameter space.Two transient stages of phase synchronisation and partial synchronisation are observed in a comparatively weak feedback coupling parameter regime,whilst complete synchronisation of spirals is found with strong negative couplings.Detailed observations of the synchronous process,such as oscillatory frequencies,parameters mismatches and amplitude variations,etc,are investigated via numerical simulations.     

FitzHugh-Nagumo系统中螺旋波的控制

采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进 关键词： 螺旋波 相空间压缩 FitzHugh-Nagumo方程     

耦合复金兹堡-朗道(Ginzburg-Landau)方程中的模螺旋波

以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.     

Amplitude wave in one-dimensional complex Ginzburgben Landau equation

The wave propagation in the one-dimensional complex Ginzburg-Landau equation (CGLE) is studied by considering a wave source at the system boundary. A special propagation region, which is an island-shaped zone surrounded by the defect turbulence in the system parameter space, is observed in our numerical experiment. The wave signal spreads in the whole space with a novel amplitude wave pattern in the area. The relevant factors of the pattern formation, such as the wave speed, the maximum propagating distance and the oscillatory frequency, are studied in detail. The stability and the generality of the region are testified by adopting various initial conditions. This finding of the amplitude pattern extends the wave propagation region in the parameter space and presents a new signal transmission mode, and is therefore expected to be of much importance.     

Synchronizing spiral waves in a coupled Rossler system

The synchronisation of spiral patterns in a drive-response R6ssler system is studied. The existence of three types of synchronisation is revealed by inspecting the coupling parameter space. Two transient stages of phase synchronisation and partial synchronisation are observed in a comparatively weak feedback coupling parameter regime, whilst complete synchronisation of spirals is found with strong negative couplings. Detailed observations of the synchronous process, such as oscillatory frequencies, parameters mismatches and amplitude variations, etc, are investigated via numerical simulations.     

Hindmarsh-Rose混沌神经元自适应同步和参数识别的优化研究

以Hindmarsh-Rose混沌神经元模型为例,讨论了基于自适应同步识别混沌系统多个参数方法的优化问题.在构造的李亚普诺夫函数中引入可调节的增益系数来控制系统同步和参数观测器的暂态过程长短.在应用单个控制器和5个参数观测器来同步和识别Hindmarsh-Rose混沌神经元中5个未知参数时发现最小参数的识别结果出现了振荡而其他参数都能准确识别现象,分析其原因可能在于要识别的目标参数的巨大差异性.通过增加控制器的个数(选择两个控制器)可以克服这个困难.研究发现增益系数太小不能实现完全同步和参数的准确识别,当增益系数太大则延长了识别参数的暂态过程.在恰当的增益系数下可以在比较短的暂态过程下准确识别系统参数.进一步讨论了系统参数发生阶跃变化时系统参数的识别问题,数值计算结果验证了该方法的可靠性和有效性.