Multi-Wing Butterfly Bursting Attractors In Alternating Current- Driven Circuit System With The Pulse Function Control

In this paper, we focus on investigating the fast-slow dynamics and complex behaviors of multi-wing butterfly bursting attractors in an alternating current (AC)-driven Lü circuit controlled by a pulse function. We treat the periodic AC perturbation as a slow-varying control parameter to tune the system's multi-scale dynamics, rather than merely using it as a critical bifurcation value for characterizing dynamical behaviors. By introducing a single or multiple pulse functions into the third equation of the Lü circuit system, additional equilibrium points are generated, laying the foundation for the evolution of multi-wing bursting. With the variation of the periodic perturbation, the system exhibits fast-slow dynamics characterized by transitions among different strange attractors, including periodic or chaotic multi-wing attractors. Notably, when the periodic perturbation induces complex oscillations containing multi-scroll chaotic components, a distinct delayed supercritical pitchfork bifurcation behavior emerges; this delayed bifurcation dynamic terminates in different parameter regions, leading to diverse spiking modes around various stable attractors, including equilibria, limit cycles, and chaotic trajectories. Our results enrich the research on bursting dynamics in AC-driven nonlinear systems, deepen the understanding of multi-wing bursting phenomena, and provide a theoretical basis for the control and application of multi-wing attractors.