Modeling nonlinear dissipative chemical dynamics by a forced modified van der Pol-Duffing oscillator with asymmetric potential: chaotic behaviors predictions. (English) Zbl 07819495
Summary: This paper addresses the issues of nonlinear chemical dynamics modeled by a modified Van der Pol-Duffing oscillator with asymmetric potential. The Melnikov method is utilized to analytically determine the domains boundaries where Melnikov’s chaos appears in chemical oscillations. Routes to chaos are investigated through bifurcations structures, Lyapunov exponent, phase portraits and Poincaré section. The effects of parameters in general and in particular the effect of the constraint parameter \(\beta\) which shows the difference between a nonlinear chemical dynamics order two differential equation and ordinary Van der Pol-Duffing equation are analyzed. Results of analytical investigations are validated and complemented by numerical simulations.
MSC:
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
Keywords:
forced modified van der Pol-Duffing oscillator; nonlinear dissipative chemical dynamics; Melnikov’s chaos; bifurcation; basin of attraction; dissipative chaosReferences:
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