期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 428, 期 2, 页码 817-837出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2015.03.045
关键词
Ratio-dependent; Refuge; Filippov system; Finite time stable
资金
- National Natural Science Foundation of China [11371127]
- China Scholarship Council
In this paper, a Filippov ratio-dependent predator-prey model is proposed to describe the effect on behavioral refuges caused by prey instinct anti-predator behavior. The proposed model extends the classical ratio-dependent predatorprey model by combining a prey-predator ratio that describes the behavioral refuges make sense once it is less than a certain threshold. One of the prominent mathematical features of our model, distinguishing from the classical one, is that there exist singular points on discontinuous surface whose characteristics determine the main dynamical behaviors of this model. The complete analysis of topological structures of orbits near all the singular points is presented. We show 14 types of system behaviors realized for various parameter values. In particular, globally stable pseudo-equilibrium and globally finite time stable canard cycle are shown to exist in some ranges of parameter values, which cannot be achieved in classical model. (C) 2015 Elsevier Inc. All rights reserved.
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