Souza Everton G, Viana Ricardo L, Lopes Sérgio R
Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, Paraná, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066206. doi: 10.1103/PhysRevE.78.066206. Epub 2008 Dec 10.
Hyperchaos occurs in a dynamical system with more than one positive Lyapunov exponent. When the equations governing the time evolution of the dynamical system are known, the transition from chaos to hyperchaos can be readily obtained when the second largest Lyapunov exponent crosses zero. If the only information available on the system is a time series, however, such method is difficult to apply. We propose the use of recurrence quantification analysis of a time series to characterize the chaos-hyperchaos transition. We present results obtained from recurrence plots of coupled chaotic piecewise-linear maps and Chua-Matsumoto circuits, but the method can be applied as well to other systems, even when one does not know their dynamical equations.
超混沌出现在具有多个正李雅普诺夫指数的动力系统中。当控制动力系统时间演化的方程已知时，当第二大李雅普诺夫指数穿过零时，就可以很容易地得到从混沌到超混沌的转变。然而，如果关于该系统的唯一可用信息是一个时间序列，那么这种方法就很难应用。我们建议使用时间序列的递归量化分析来表征混沌 - 超混沌转变。我们展示了从耦合混沌分段线性映射和蔡 - 松本电路的递归图中获得的结果，但即使不知道其动力学方程，该方法也同样可以应用于其他系统。
