Influence of Control Parameters on the Competition Between Spiral Waves and Target Waves

In this paper we systematically investigate the influence of control parameters on the competition results between spiral waves and target waves. Driving frequency f , amplitude A and injection area n of the input signals are three important parameters and the competition results between spiral waves and target waves are influenced by these three parameters remarkably. Based on these understandings we can control spiral waves effectively by suitable combination these parameters to generate faster target waves. And the effective controllable parameter regions are also studied.     

Attractive target wave patterns in complex networks consisting of excitable nodes

This review describes the investigations of oscillatory complex networks consisting of excitable nodes,focusing on the target wave patterns or say the target wave attractors.A method of dominant phase advanced driving(DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations,such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks.The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns.Therefore,the center(say node A) and its driver(say node B) of a target wave can be used as a label,(A,B),of the given target pattern.The label can give a clue to conveniently retrieve,suppress,and control the target waves.Statistical investigations,both theoretically from the label analysis and numerically from direct simulations of network dynamics,show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large,and all these attractors can be labeled and easily controlled based on the information given by the labels.The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.     

时空调制对可激发介质螺旋波波头动力学行为影响及控制研究

本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响. 随着时空调制的增大, 螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化. 通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件, 及漫游螺旋波波头圆滚圆半径随调制参数的变化情况. 当时空调制增大到某个临界值时, 螺旋波发生了破碎; 再增加时空调制, 螺旋波则发生了衰减, 系统最终演化为空间均匀静息态. 在文中给出了螺旋波发生破碎和衰减的机理和原因. 最后将时空调制方法运用于漫游螺旋波, 实现了将漫游螺旋波控制成周期螺旋波, 或将其控制为空间均匀静息态.     

Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

Self-sustained oscillations in complex networks consisting of nonoscillatory nodes have attracted long-standing interest in diverse natural and social systems. We study the self-sustained periodic oscillations in random networks consisting of excitable nodes. We reveal the underlying dynamic structure by applying a dominant phase-advanced driving method. The oscillation sources and wave propagation paths can be illustrated clearly via the dynamic structure revealed. Then we are able to control the oscillations with surprisingly high efficiency based on our understanding.     

The influence of long-range links on spiral waves and their application for control

The influence of long-range links on spiral waves in an excitable medium has been investigated.Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P.Spiral waves with few perturbations,broken spiral waves,pseudo spiral turbulence,synchronous oscillations,and homogeneous rest state are discovered under different network structures.Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns.The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state.Finally,we use long-range links to successfully control spiral waves and spiral turbulence.     

The influence of long-range links on spiral waves and its application for control

The influence of long-range links on spiral waves in excitable medium has been investigated. Spatiotemporal dynamics in excitable small-world network transforms remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to control spiral wave and spiral turbulence successfully.     

Doppler instability of antispiral waves in discrete oscillatory reaction-diffusion media

This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh-Nagumo cells with self-sustained oscillation via Hopf bifurcation.When the coupling strength of the active variable decreases to a critical value,wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence.Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.     

可激发介质湍流的耦合同步及控制

利用相互耦合方法实现了两个处于湍流态的可激发系统的精确同步，给出了确定耦合系数的方法，计算了最大横向Lyapunov指数.并基于相互耦合，将处于湍流态的可激发系统与两个处于不同状态的可激发系统进行相互耦合，实现了用两种不同方法对湍流态的稳定控制. 关键词： 可激发介质 湍流控制 同步 耦合系数     

不同缺陷对周期螺旋波的影响

研究了不同单个圆形缺陷对周期螺旋波的影响。数值模拟发现,如果缺陷中心不变,那么,它对周期螺旋波的影响存在两个临界半径rd1和rd2。当缺陷半径rd=rd1时,波头的最终运动轨迹会发生远离缺陷的幅度较大的漂移;当rd=rd2时,波头在缺陷产生后经过一段时间的演化会消失。数值模拟同时发现,rd1和缺陷中心到波头中心的距离d一一对应;同样,rd2也和d一一对应,且都随d线性增大。     

Dominant phase-advanced driving analysis of self-sustained oscillations in biological networks

Oscillatory behaviors can be ubiquitously observed in various systems. Biological rhythms are significant in governing living activities of all units. The emergence of biological rhythms is the consequence of large numbers of units. In this paper we discuss several important examples of sustained oscillations in biological media, where the unit composed in the system does not possess the oscillation behavior. The dominant phase-advanced driving method is applied to study the skeletons and oscillatory organizing motifs in excitable networks and gene regulatory networks.