Bifurcation analysis of a three-species ecological system with time delay and harvesting

This paper deals with a three-species ecological system with time delay and harvesting. Sufficient conditions guaranteeing the local stability and the occurrence of Hopf bifurcation for the system are obtained. Further, the properties of Hopf bifurcation are investigated using the center manifold th...

Full description

Saved in:
Bibliographic Details
Published inAdvances in difference equations Vol. 2017; no. 1; pp. 1 - 12
Main Authors Zhang, Zizhen, Wan, Aying
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 24.10.2017
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Bifurcation theory
Computer simulation
Delay
Difference and Functional Equations
Ecological monitoring
ecological system
Economic models
Ecosystems
Functional Analysis
Harvesting
Hopf bifurcation
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
periodic solution
Time lag
periodic solution
34C15
delay
34C23
37N25
ecological system
Hopf bifurcation
37G15
Online AccessGet full text

Cover

More Information
Summary:This paper deals with a three-species ecological system with time delay and harvesting. Sufficient conditions guaranteeing the local stability and the occurrence of Hopf bifurcation for the system are obtained. Further, the properties of Hopf bifurcation are investigated using the center manifold theorem and normal form theory. Computer simulations are carried out to illustrate the theoretical predictions. Finally, biological meaning and a conclusion are presented.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-017-1393-x