title: Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response.
abstract: Predator-prey models with Michaelis-Menten-Holling type ratio- dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and heteroclinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator-prey model. We first calculate the higher order Melnikov functions by transforming the model into a Hamiltonian system and then provide an algorithm for computing higher order approximations of the heteroclinic bifurcation curves.
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA. ruan@math.miami.edu
authors.forename: Shigui
authors.initials: S
authors.lastname: Ruan
authors.forename: Yilei
authors.initials: Y
authors.lastname: Tang
authors.forename: Weinian
authors.initials: W
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011235:Predatory Behavior