Periodic Oscillation of the Solutions for a Parkinson's Disease Model

Abstract

In this paper, the oscillation of the solutions for a Parkinson's disease model with multiple delays is discussed. By linearizing the system at the equilibrium point and analyzing the instability of the linearized system, some sufficient conditions to guarantee the existence of periodic oscillation of the solutions for a delayed Parkinson's disease system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate our theoretical prediction.