Effect of bounded noise on the chaotic motion of a Duffing Van der pol oscillator in a φ⁶ potential

This paper investigates the chaotic behavior of an extended Duffing Van der pol oscillator in a φ⁶ potential under additive harmonic and bounded noise excitations for a specific parameter choice. From Melnikov theorem, we obtain the conditions for the existence of homoclinic or heteroclinic bifurcation in the case of the φ⁶ potential is bounded, which are complemented by the numerical simulations from which we illustrate the bifurcation surfaces and the fractality of the basins of attraction. The results show that the threshold amplitude of bounded noise for onset of chaos will move upwards as the noise intensity increases, which is further validated by the top Lyapunov exponents of the original system. Thus the larger the noise intensity results in the less possible chaotic domain in parameter space. The effect of bounded noise on Poincare maps is also investigated.