An Alternative Approach for Identifying Nonlinear Dynamics of the Cascade Logistic-Cubic System

The 0-1 test for chaos, which is a simple binary method, has been widely used to detect the nonlinear behaviors of non-cascade chaotic dynamics. In this paper, validity checks chaos popular cascade Logistic-Cubic (L-C) system conducted through exploring effects sensitivity parameters. Results show that periodic, weak-chaotic, and strong-chaotic states L-C can be effectively identified by introduced method detecting chaos. Nevertheless, two parameters, including frequency ω amplitude α, are critical indicator (i.e., median asymptotic growth rate, Km) when dynamic detected method. It found effect α more sensitive than on Km regarding three dynamical system. Meanwhile, it recommended according change K with from zero ten since periodic weak-chaotic cannot greater certain constant. addition, modified mean square displacement Dc*(n) fails distinguish its states, whereas obviously above states. This work therefore invaluable gaining insight into understanding complex nonlinearity other different systems comparison.