On a diffusive predator-prey model with nonlinear harvesting | Zendy

Peng Feng | Zendy

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On a diffusive predator-prey model with nonlinear harvesting

Author(s) -

Peng Feng

Publication year - 2014

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2014.11.807

Subject(s) - nonlinear system , term (time) , stability (learning theory) , lyapunov function , mathematics , instability , exponential stability , control theory (sociology) , statistical physics , computer science , physics , mechanics , control (management) , quantum mechanics , machine learning , artificial intelligence

In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

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