Dynamic Behavior for a Coupled Nonlinear Oscillator Model with Distributed and Discrete Delays

Abstract

— In this paper, the oscillatory behavior of the solutions for a coupled nonlinear oscillator model with distributed and discrete delays is investigated. Time delay induced partial death patterns with conjugate coupling in relay oscillators has been investigated in the literature. According to the practical problem, the propagation delays are not only the discrete delays, but also with distributed delay. A model includes distributed and discrete delays is considered. By mathematical analysis method, the oscillatory behavior of the coupled nonlinear oscillator model is brought to the instability of the uniqueness equilibrium point and the boundedness of the solutions. Some sufficient conditions are provided to guarantee the oscillation of the solutions. Computer simulations are given to support the present results. Our simulation suggests that the two theorems are only sufficient conditions.