Bifurcation and Chaos Analysis of Coupled Duffing Oscillators with Two-Periodic Excitations and Distributed Time Delays

This paper employs both analytical and numerical methods to investigate the dynamic characteristics of a coupled Duffing oscillators with two-periodic excitations and distributed time delays. First, the original system is transformed to an equivalent slow-coupled system using the fast–slow analysis method. The stability of equilibrium points and the pitchfork bifurcation phenomena resulting from changes in parameters are analyzed. Specifically, the relationship between the number of coupling layers and the stable equilibrium points is explored. Subsequently, the necessary conditions for the occurrence of chaos, such as homoclinic bifurcation leading to horseshoe chaos, are derived using the Melnikov method. By integrating phase diagrams with the largest Lyapunov exponent, we analyzed the influence of various parameters on chaotic trajectories. Additionally, the specific effects of system distribution delay intensity were further illustrated through numerical simulations.