Chameleon Chaotic Dynamics in a Modified Duffing System

This paper investigates the chaotic dynamics of a modified Duffing system with symmetry, focusing on the transitions between self-excited and hidden attractors as some parameters vary. By simplifying and modifying the Duffing equation, we proposed a new chameleon chaotic system with symmetry and supercritical Hopf bifurcation. The two main parameters in this system are [Formula: see text] and [Formula: see text], which represent the driving frequency and the initial phase, respectively. Recall that chameleon systems can alternate their chaotic attractors between hidden and self-excited types by varying system parameters. We investigate the basic properties of the system, including dissipativity, local stability of equilibrium point, and type of Hopf bifurcation. By varying the parameter [Formula: see text], we observe two types of flows: self-excited and hidden. A similar yet more detailed exploration is conducted for the parameter [Formula: see text]. This latter exploration primarily focuses on the following aspects: self-excited and hidden dynamics, extreme multistability at [Formula: see text], and the transition zone near [Formula: see text]. For the hidden chaotic case with a stable node-focus at [Formula: see text], we first conducted PSpice circuit simulation and then performed digital hardware implementation based on STM32 microcontroller, thus verifying the feasibility of this system from both software simulation and physical realization perspectives.