Title :
Hopf bifurcation in a three stage-structured prey-predator model with hunting delay
Author :
Li, Shunyi ; Liu, Wenwu
Author_Institution :
Dept. of Math., Qiannan Normal Coll. for Nat., Duyun, China
Abstract :
A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical simulation and brief conclusion are given.
Keywords :
Nyquist criterion; bifurcation; delays; numerical analysis; predator-prey systems; Hopf bifurcation; Nyquist criterion; boundary equilibrium; characteristic equations; hunting delay; length estimation; numerical simulation; positive equilibrium; stability preservation; three stage-structured prey-predator model; Asymptotic stability; Bifurcation; Delay; Delay effects; Stability criteria; Hopf bifurcation; Three-stage-structured; prey-predator model; time delay;
Conference_Titel :
Systems and Informatics (ICSAI), 2012 International Conference on
Conference_Location :
Yantai
Print_ISBN :
978-1-4673-0198-5
DOI :
10.1109/ICSAI.2012.6223231
