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

Yanan Liao, Kai Yang, Hua Wang and Qingtai Xiao
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Yanan Liao: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China
Kai Yang: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China
Hua Wang: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China
Qingtai Xiao: State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China

Mathematics, 2022, vol. 10, issue 12, 1-13

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

Keywords: 0-1 test for chaos; sensitivity parameter; cascade dynamic system; Logistic-Cubic mapping; noised time series analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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