Synchronization control of stochastic delayed Lotka\u2013Volterra systems with hardware simulation

Lan Wang,Da Xie,Hao Zhang,Yiping Dong

doi:10.1186/s13662-019-2474-9

Abstract

In this paper, the synchronization control of a non-autonomous Lotka–Volterra system with time delay and stochastic effects is studied. The purpose is to firstly establish sufficient conditions for the existence of global positive solution by constructing a suitable Lyapunov function. Some synchronization criteria are then derived by designing an appropriate full controller and a pinning controller, respectively. Finally, an example is presented to illustrate the feasibility and validity of the main theoretical results based on the Field-Programmable Gate Array hardware simulation tool.

Highlights

The Lotka–Voltera (LV) system is one of the famous biological models which describe the interaction of a predator–prey model and consist of nonlinear ordinary differential equations, developed by Lotka and Volterra [1]
Over the past 20 years, the LV system has been extensively investigated from different aspects such as stability, control, evolutionary dynamics [2,3,4,5,6,7]
The global dynamics of a classical LV system was investigated with the effects of competition ability and impulsive periodic disturbance in Refs. [6, 7]

Summary

Introduction

The Lotka–Voltera (LV) system is one of the famous biological models which describe the interaction of a predator–prey model and consist of nonlinear ordinary differential equations, developed by Lotka and Volterra [1]. Over the past 20 years, the LV system has been extensively investigated from different aspects such as stability, control, evolutionary dynamics [2,3,4,5,6,7]. Based on many natural predator–prey interactions which sometimes exhibit stability, Ref. [3] checked the effect of small immigration and the inclusion of a nonlinear interaction term to the stability of the LV system. The global dynamics of a classical LV system was investigated with the effects of competition ability and impulsive periodic disturbance in Refs. Time delays are ubiquitous in the processing of information transmission because of the limited resource and environmental disturbance, which may cause undesired dynamics like oscillation, bifurcation and instability.

Objectives

Conclusion