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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

A prey-predator model with migrations and delays

Pages: 737 - 761, Volume 21, Issue 3, May 2016      doi:10.3934/dcdsb.2016.21.737

 
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Isam Al-Darabsah - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, A1C 5S7, Canada (email)
Xianhua Tang - School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China (email)
Yuan Yuan - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, Canada A1C 5S7, Canada (email)

Abstract: In this paper we propose a prey-predator model in multiple patches through the stage structured maturation time delay with migrations among patches. Focus on the case with two patches, we discuss the existence of equilibrium points and the uniform persistence. In particular, when the maturation times are the same in the patches, we study the local and global attractivity of boundary equilibrium point with general migration function and the local stability of the positive equilibrium with constant migration rate. Numerical simulations are provided to demonstrate the theoretical results, to illustrate the effect of the maturation time, the migration rate on the dynamical behavior of the system.

Keywords:  Prey-predator, time delay, prey/predator migration, equilibrium points, uniform persistence, stability.
Mathematics Subject Classification:  Primary: 34D20, 92D25; Secondary: 92D40.

Received: January 2015;      Revised: September 2015;      Available Online: January 2016.

 References