Recurrence Network-Based Approach to Distinguish Between Chaotic and Quasiperiodic Solution

Abstract

The quasiperiodic route to chaos is observed in many complex dynamical systems. Quasiperiodic solutions have many similar features of a chaotic system, making it difficult to distinguish between them. In this paper, we propose a complex network-based method for differentiating quasiperiodic from chaotic solutions. The efficiency of the method is demonstrated using chaotic and quasiperiodic realisations generated from two dynamical systems, Chua’s circuit and Lorenz system involving complex variables. Statistical analysis of the networks generated from time series shows that there is a significant difference between the network characteristics of quasiperiodic and chaotic dynamics.