IJPAM: Volume 95, No. 4 (2014)

HOPF BIFURCATION AND GLOBAL PERIODIC SOLUTION
IN A DELAYED STAGE-STRUCTURED
PREY-PREDATOR SYSTEM

Shunyi Li$^1$, Yu Wei$^2$, Wenwu Liu$^3$
$^{1,2,3}$Department of Mathematics
Qiannan Normal College for Nationalities
Duyun, Guizhou, 558000, P.R. CHINA


Abstract. A prey-predator model with stage-structured for predator and time delay is considered. The characteristic equations of the equilibrium points are analyzed, by applying the theorem of Hopf bifurcation, the conditions for the positive equilibrium occurring local Hopf bifurcation are given. The conditions for the existence of global Hopf bifurcation of the system are obtained. Finally, numerical simulation and brief conclusion are given.

Received: March 31, 2013

AMS Subject Classification: 34K13, 34K18, 34K20, 34K60, 92D25

Key Words and Phrases: prey-predator system, stage-structured, time delay, Hopf bifurcation, global periodic solution

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DOI: 10.12732/ijpam.v95i4.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 4
Pages: 493 - 502


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