Spatiotemporal Patterns of a Homogeneous Diffusive Predator–Prey System with Holling Type III Functional Response

The dynamics of a diffusive predator–prey system with Holling type-III functional response subject to Neumann boundary conditions is investigated. The parameter region for the stability and instability of the unique constant steady state solution is derived, and the existence of time-periodic orbits...

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Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 29; no. 4; pp. 1383 - 1409
Main Author Wang, Jinfeng
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Bifurcation theory
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Stability
Steady state
Leray–Schauder degree
Hopf bifurcation
Global stability
Steady state solution
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Summary:The dynamics of a diffusive predator–prey system with Holling type-III functional response subject to Neumann boundary conditions is investigated. The parameter region for the stability and instability of the unique constant steady state solution is derived, and the existence of time-periodic orbits and non-constant steady state solutions are proved by bifurcation method and Leray–Schauder degree theory. The effect of various parameters on the existence and nonexistence of spatiotemporal patterns is analyzed. These results show that the impact of Holling type-III response essentially increases the system spatiotemporal complexity.
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ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-016-9517-7