Viana RL, Grebogi C
Departamento de Fisica, Universidade Federal do Parana, 81531-990, Curitiba, PR, Brazil.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1 Pt A):462-8. doi: 10.1103/physreve.62.462.
The nonhyperbolic structure of synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits an unstable dimension variability, which is an extreme form of nonhyperbolicity. We analyze the dynamics in the synchronization manifold and in its transversal direction, where a tonguelike structure is formed, through a system of two coupled chaotic maps. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values. We also point out that unstable dimension variability is a cause of severe modeling difficulty.
本研究探讨了同步动力学的非双曲结构。我们通过分析论证并通过数值验证，同步流形上的混沌动力学表现出不稳定的维度变异性，这是一种极端形式的非双曲性。我们通过一个由两个耦合混沌映射组成的系统，分析了同步流形及其横向方向上的动力学，其中形成了一个舌状结构。在有限时间横向李雅普诺夫指数的统计分布中揭示了不稳定的维度变异性，该指数具有正负值。我们还指出，不稳定的维度变异性是造成严重建模困难的一个原因。
