A Simple Nonautonomous Hidden Chaotic System with a Switchable Stable Node-Focus

Abstract

This paper presents a simple two-dimensional nonautonomous system, which possesses piecewise linearity constructed by a simple absolute value function. The nonautonomous system has only one switchable equilibrium state with a stable node-focus in the considered control parameter region but can generate periodic, chaotic and coexisting attractors. Therefore, the presented simple two-dimensional nonautonomous system always operates with hidden oscillations, which is not similar to any example reported in the literature. Furthermore, specific hidden dynamical behaviors are numerically disclosed by employing one-dimensional and two-dimensional bifurcation plots, phase plane plots, Poincaré mappings, local attraction basins, and complexity plots. In addition, by utilizing the circuit module of the absolute value function, a multiplierless analog circuit is designed, based on which breadboard experiments are performed to validate the numerically simulated phase plane plots of coexisting attractors.