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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 223-241 |
| Number of pages | 19 |
| Journal | Journal of Mathematical Biology |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 1 2008 |
Keywords
- Approximation
- Beta functions
- Hamiltonian system
- Heteroclinic loop
- Melnikov functions
- Predator-prey system
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
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Cite this
Ruan, S., Tang, Y., & Zhang, W. (2008). Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response. Journal of Mathematical Biology, 57(2), 223-241. https://doi.org/10.1007/s00285-007-0153-z