Diffusion-driven stability and bifurcation in a predator-prey system with Ivlev-type functional response

Applicable Analysis

Volumn 92, Issue 4, 2013, Pages 752-775

  Wang, Xuechen ^a   Wei, Junjie ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

diffusion; Hopf bifurcation; Ivlev type functional response; periodic solutions; prey predator system

Indexed keywords

EID: 84874617906     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036811.2011.635656     Document Type: Article

References (17)

1. Ivlev, VS. 1961. Experimental Ecology of the Feeding of Fishes, New Haven: Yale University Press.
2. Garvie, MR. 2007. Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB. Bull. Math. Biol., 69: 931-956.
3. May, RM. 1973. Complexity and Stability in Model Ecosystems, Princeton, NJ: Princeton University Press.
4. Metz, J and Diekmann, O. 1986. "A gentle introduction to structured population models: Three worked examples". In The Dynamics of Physiologically Structured Populations (Lecture Notes in Biomathematics 68), Edited by: Metz, JAJ and Diekmann, O. 3-45. Berlin: Springer.
5. Kooij, R and Zegeling, A. 1996. A predator-prey model with Ivlev's functional response. J. Math. Anal. Appl., 198: 473-489.
6. Sugie, J. 1998. Two-parameter bifurcation in a predator-prey system of Ivlev-type. J. Math. Anal. Appl., 217: 349-371.
7. Tian, RC. 2006. Toward standard parameterizations in marine biological modeling. Ecol. Model., 193: 363-386.
8. Wang, H and Wang, W. 2007. The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect. Chaos Solitons Fractals, 38: 1168-1176.
9. Preedy, KF, Schofield, PG, Chaplain, MAJ and Hubbard, SF. 2007. Disease induced dynamics in host-parasitoid systems: Chaos and coexistence. J. R. Soc. Interf., 4: 463-471.
10. Sherratt, JA, Lewis, MA and Fowler, AC. 1995. Ecological chaos in the wake of invasion. Proc. Nat. Acad. Sci. USA, 92: 2524-2528.
11. Sherratt, JA, Eagan, BT and Lewis, MA. 1997. Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?. Philos. Trans. R. Soc. B: Biol. Sci., 352: 21-38.
12. Kay, AL and Sherratt, JA. 2000. Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains. SIAM J. Appl. Math., 61: 1013-1041.
13. Pearce, IG, Chaplain, MAJ, Schofield, PG, Anderson, ARA and Hubbard, SF. 2006. Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: Heterogeneous patterns and ecological implications. J. Theor. Biol., 241: 876-886.
14. Uriu, K and Iwasa, Y. 2007. Turing pattern formation with two kinds of cells and a diffusive chemical. Bull. Math. Biol., 69: 2515-2536.
15. Wang, W, Zhang, L, Wang, H and Li, Z. 2010. Pattern formation of a predator-prey system with Ivlev-type functional response. Ecol. Model., 221: 131-140.
16. Hassard, BD, Kazarinoff, ND and Wan, YH. 1981. Theory and applications of Hopf bifurcation, Cambridge, MA: CUP Archive.
17. Yi, F, Wei, J and Shi, J. 2009. Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system. J. Differ. Eqns, 246: 1944-1977.