Canard explosion,homoclinic and heteroclinic orbits in singularly perturbed generalist predator-prey systems  

作　　者：Ali Atabaigi 

机构地区：[1]Department of Mathematics,Razi University,Kermanshah,Iran

出　　处：《International Journal of Biomathematics》2021年第1期151-174,共24页生物数学学报（英文版）

摘　　要：This paper studies the dynamics of the generalist predator–prey systems modeled in[E.Alexandra,F.Lutscher and G.Seo,Bistability and limit cycles in generalist predator–prey dynamics,Ecol.Complex.14(2013)48–55].When prey reproduces much faster than predator,by combining the normal form theory of slow-fast systems,the geometric singular perturbation theory and the results near non-hyperbolic points developed by Krupa and Szmolyan[Relaxation oscillation and canard explosion,J.Differential Equations174(2)(2001)312–368;Extending geometric singular perturbation theory to nonhyperbolic points—fold and canard points in two dimensions,SIAM J.Math.Anal.33(2)(2001)286–314],we provide a detailed mathematical analysis to show the existence of homoclinic orbits,heteroclinic orbits and canard limit cycles and relaxation oscillations bifurcating from the singular homoclinic cycles.Moreover,on global stability of the unique positive equilibrium,we provide some new results.Numerical simulations are also carried out to support the theoretical results.

关 键 词：Canard cycle relaxation oscillation generalist predator prey singular perturbation HOMOCLINIC HETEROCLINIC 

分 类 号：O17[理学—数学]