Melnikov chaos in a periodically driven Rayleigh–Duffing oscillator

The chaotic behavior of Duffing–Rayleigh oscillator under harmonic external excitation is investigated. Melnikov technique is used to detected the necessary conditions for chaotic motion of this deterministic system. The results show that the shape of the basin boundaries of attraction are fractals as the damping increases above the threshold of Melnikov chaos. The effect of damping parameter on phase portraits and Poincaré maps, in addition to the numerical simulations of bifurcation diagram and maximum Lyapunov exponents is also investigated.