Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits
Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits
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DOI：
10.1002/cta.213
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发表时间：
2002-11
影响因子：
2.3
通讯作者：
B. Cannas;S. Cincotti
中科院分区：
文献类型：
--
作者：
B. Cannas;S. Cincotti
本文提出了两个蔡氏电路的非线性双向耦合。耦合是通过使用多项式函数是对称的两个蔡氏电路的状态变量。为了保证结果在状态空间中的全局有效性，对横截系统和切向系统都进行了研究。首先，它示出的横向系统是一个自治的蔡氏电路，它直接允许其混沌行为，即耦合电路之间的同步的情况下的条件的评价。此外，还证明了切向系统也是一个蔡氏回路，受横向系统的强迫;因此，其动力学由一个时间依赖方程控制。因此，条件李雅普诺夫指数的演算是必要的，以排除反同步沿着切流形。
In this paper, a non‐linear bi‐directional coupling of two Chua's circuits is presented. The coupling is obtained by using polynomial functions that are symmetric with respect to the state variables of the two Chua's circuits. Both a transverse and a tangent system are studied to ensure a global validity of the results in the state space. First, it is shown that the transverse system is an autonomous Chua's circuit, which directly allows the evaluation of the conditions on its chaotic behaviour, i.e. the absence of synchronization between the coupled circuits. Moreover, it is demonstrated that the tangent system is also a Chua's circuit, forced by the transverse system; therefore, its dynamics is ruled by a time‐dependent equation. Thus, the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold.