Exploring Chameleon Chaos: A Linearly Modulated Generalized Duffing System with Hidden and Self-Excited Attractors

This paper presents a novel chameleon chaotic system derived from a generalized Duffing oscillator, where the linear damping parameter [Formula: see text] controls the transition between hidden and self-excited attractors. The investigation covers the system’s basic properties, including symmetries, dissipativity, and equilibrium stability, where the stability analysis identifies a supercritical Hopf bifurcation at [Formula: see text] as the transition mechanism. This bifurcation helps to find two potential dynamical regimes: for [Formula: see text], the system may exhibit hidden attractors coexisting with a stable equilibrium; for [Formula: see text], self-excited attractors can arise from the unstable equilibrium. By setting several parameters to fixed values, including the critical condition [Formula: see text], we define the model’s reduced system with an elegant form. A detailed analysis of this system using bifurcation and continuation diagrams, Lyapunov exponents, return map, and power spectrum shows the existence of a hidden chaotic attractor and reveals rich multistability behavior. Bifurcation studies across multiple parameter planes demonstrate period-doubling cascades to chaos, periodic windows, and complex dynamical landscapes. Finally, the phase portraits produced by an FPGA-based realization closely match numerical simulations, thus enabling our manageability of the chameleon dynamics.