Dynamic analysis of a reaction-diffusion impulsive hybrid system. (English) Zbl 1433.35424
Summary: In this paper, a predator-prey system with Crowley-Martin functional response, which is described by a couple of reaction-diffusion equations with impulsive effect, is studied analytically and numerically. The aim of this research is to analyze how the impulsive effect influences dynamics of the system. Dynamics of the system, including the ultimate boundedness, permanence and extinction, are investigated firstly under impulsive effects. Significantly, it is found that there exists a unique positive periodic solution that is globally asymptotically stable when impulsive effects reach some critical state. Additionally, a series of numerical simulations are carried out to further study the dynamics of the system, which are consistent with the analytical results.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 35B10 | Periodic solutions to PDEs |
| 35B09 | Positive solutions to PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 65G40 | General methods in interval analysis |
Keywords:
Crowley-Martin functional response; reaction-diffusion equation; permanence; periodic solution; impulsive effectReferences:
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