Zhao Liang, Lai Ying-Cheng, Shih Chih-Wen
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):036212. doi: 10.1103/PhysRevE.72.036212. Epub 2005 Sep 19.
Coupled chaotic oscillators can exhibit intermittent synchronization in the weakly coupling regime, as characterized by the entrainment of their dynamical variables in random time intervals of finite duration. We find that the transition to intermittent synchronization can be characteristically distinct for geometrically different chaotic attractors. In particular, for coupled phase-coherent chaotic attractors such as those from the Rössler system, the transition occurs immediately as the coupling is increased from zero. For phase-incoherent chaotic attractors such as those in the Lorenz system, the transition occurs only when the coupling is sufficiently strong. A theory based on the behavior of the Lyapunov exponents and unstable periodic orbits is developed to understand these distinct transitions.
耦合混沌振子在弱耦合状态下能够表现出间歇性同步，其特征是它们的动力学变量在有限持续时间的随机时间间隔内产生同步。我们发现，对于几何形状不同的混沌吸引子，向间歇性同步的转变可能具有显著差异。特别是，对于诸如来自罗斯勒系统的耦合相位相干混沌吸引子，当耦合从零增加时，转变会立即发生。对于诸如洛伦兹系统中的相位非相干混沌吸引子，只有当耦合足够强时才会发生转变。基于李雅普诺夫指数和不稳定周期轨道的行为发展了一种理论，以理解这些不同的转变。
