Resonance oscillation and transition to chaos in \(\phi^8\)-Duffing-van der Pol oscillator
Following the study of a Duffing-Van der Pol oscillator of which the potential function is a polynomial of degree six, the author extend his investigation of the oscillator to the potential function of degree eight. It seems that the new system exhibits much richer nonlinear behavior than the previous one. From numerical simulations, even though the system with degree six is stable, a small value of the coefficient of the degree-eight term already induces very complex dynamical behavior such as the coexistence of multiple limit cycles, period-doubling route to chaos and sudden chaos. An electronic circuit was also designed to confirm to a great extent the theoretical and simulation results.
scientific article; zbMATH DE number 7490013
scientific article