关键词: nonlinear time series, unified PWL chaotic family, Lyapunov exponents, complex network

Abstract: Duality analysis of time series and complex networks has been a frontier topic during the last several decades. According to some recent approaches in this direction, the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science. In this paper, the associated network family of the unified piecewise-linear (PWL) chaotic family, which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system, was firstly constructed and analyzed. We constructed the associated network family via the original and the modified frequency-degree mapping strategy, as well as the classical visibility graph and horizontal visibility graph strategy, after removing the transient states. Typical related network characteristics, including the network fractal dimension, of the associated network family, are computed with changes of single key parameter $\alpha$. These characteristic vectors of the network are also compared with the largest Lyapunov exponent (LLE) vector of the related original dynamical system. It can be found that, some network characteristics are highly correlated with LLE vector of the original nonlinear system, i.e., there is an internal consistency between the largest Lyapunov exponents, some typical associated network characteristics, and the related network fractal dimension index. Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation, which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.

Key words: nonlinear time series, unified PWL chaotic family, Lyapunov exponents, complex network