Permanency in predator–prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response
| Autor: | H.M. Mohammadinejad, H. Qolizadeh Amirabad, Omid RabieiMotlagh |
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| Rok vydání: | 2019 |
| Předmět: |
Lyapunov function
Hopf bifurcation Numerical Analysis General Computer Science Applied Mathematics Functional response Ratio dependent 010103 numerical & computational mathematics 02 engineering and technology Type (model theory) 01 natural sciences Stability (probability) Theoretical Computer Science symbols.namesake Modeling and Simulation Limit cycle 0202 electrical engineering electronic engineering information engineering symbols Quantitative Biology::Populations and Evolution Applied mathematics 020201 artificial intelligence & image processing Limit (mathematics) 0101 mathematics Mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 157:63-76 |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2018.09.023 |
| Popis: | We consider a predator–prey model of Leslie type with ratio-dependent simplified Holling type-IV functional response. The novelty of the model is that the functional response simulates group defense of the prey kind, which in turn, affects permanency of the system and existence of limit cycles. We show that permanency of the system holds automatically for some values of parameters and provides sufficient conditions for global stability of interior equilibrium by constructing a Lyapunov function. We prove that for some values of parameters the system exhibits a Hopf cycle and provides conditions by which the corresponding stable Hopf cycle is the only cycle that model may have. Numerical simulations show that if the conditions are broken, the model may have more than one limit cycle, which is phenomenal among the predator–prey models with one interior equilibrium. |
| Databáze: | OpenAIRE |
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