On jump resonance in nonlinear and linear coupled oscillators

The behavior of nonlinear oscillators and that of compound systems formed by coupling them with other types of oscillators (nonlinear or linear) has been a topic of interest for numerous researchers, due to the complexity of observable phenomena as well as to some practical engineering applications. This paper analyzes the behavior in harmonic regime of a system formed by coupling a nonlinear Duffing type oscillator with a linear oscillator. Determining the mathematical model of this system allows analyzing the jump resonance phenomenon. The existence of an unstable functioning regime for certain values of the amplitude or frequency of the harmonic input signal means that the system is possibly evolving to chaos. We illustrate this functioning regime and we synthesize a chaos control rule. Results obtained by numerical simulation confirm our theoretical considerations.