Variable structure control for a singular biological economic model with time delay and stage structure

Advances in Difference Equations

Yudan Wei¹  Yi Zhang² 

[1] School of Automation, Nanjing University of Science and Technology, Nanjing, China;School of Science, Shenyang University of Technology, Shenyang, China

关键词: predator-prey;    singular biological economic model;    stage structure;    time delay;    variable structure control;   

DOI  :  10.1186/s13662-017-1436-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A singular biological economic model which considers a prey-predator system with time delay and stage structure is proposed in this paper. The local stability at the equilibrium point and the dynamic behavior of the model are studied. Local stability analysis of the model without time delay reveals that there is a phenomenon of singularity-induced bifurcation due to the economic equilibrium. Furthermore, the phenomenon of Hopf bifurcation of the model at the boundary equilibrium point occurs as the time delay satisfies certain conditions. In order to apply variable structure control to eliminate the complex behaviors caused by singularity-induced bifurcation, the singular model is transformed into a single-input and single-output model with parameter varying within definite intervals. Then variable structure control with sliding mode based on a power reaching law is designed to stabilize the model. Numerical simulations are given to verify the effectiveness of the conclusions.

【 授权许可】

CC BY