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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| Published in | Journal of dynamics and differential equations Vol. 29; no. 4; pp. 1383 - 1409 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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New York
Springer US
01.12.2017
Springer Nature B.V |
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| Abstract | 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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| AbstractList | 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. |
| Author | Wang, Jinfeng |
| Author_xml | – sequence: 1 givenname: Jinfeng surname: Wang fullname: Wang, Jinfeng email: jinfengwangmath@163.com organization: School of Mathematical Science, Harbin Normal University |
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| SubjectTerms | Applications of Mathematics Bifurcation theory Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Stability Steady state |
| Title | Spatiotemporal Patterns of a Homogeneous Diffusive Predator–Prey System with Holling Type III Functional Response |
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