Tangent response in coupled dynamical systems

doi:10.1088/1674-1056/19/9/090501

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90501-090501.doi: 10.1088/1674-1056/19/9/090501

Tangent response in coupled dynamical systems

闫华, 魏平, 肖先赐

School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

收稿日期:2009-12-03 修回日期:2010-03-24 出版日期:2010-09-15 发布日期:2010-09-15

Tangent response in coupled dynamical systems

Yan Hua(闫华)^†, Wei Ping(魏平), and Xiao Xian-Ci(肖先赐)

School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2009-12-03 Revised:2010-03-24 Online:2010-09-15 Published:2010-09-15

摘要/Abstract

摘要： We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.

Abstract: We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.

Key words: tangent response, generalised synchronisation, coupled dynamical systems

中图分类号:

0545

闫华, 魏平, 肖先赐. Tangent response in coupled dynamical systems[J]. 中国物理B, 2010, 19(9): 90501-090501.

Yan Hua(闫华), Wei Ping(魏平), and Xiao Xian-Ci(肖先赐). Tangent response in coupled dynamical systems[J]. Chin. Phys. B, 2010, 19(9): 90501-090501.

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Tangent response in coupled dynamical systems

Tangent response in coupled dynamical systems

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