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He, Rensheng; Xiong, Zuoliang; Hong, Desheng; Yin, Hongwei

Analysis of a stochastic ratio-dependent one-predator and two-mutualistic-preys model with Markovian switching and Holling type III functional response. (English) Zbl 1418.92093

Adv. Difference Equ. 2016, Paper No. 285, 23 p. (2016).
Summary: In this paper, we propose a stochastic ratio-dependent one-predator and two-mutualistic-preys model perturbed by white and telegraph noise. By the \(M\)-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established. These conditions are all dependent on the parameters of subsystems and the stationary probability distribution of the Markov chain. We also obtain the boundary of limit superior and inferior of the average in time of the solution under stochastic permanence. Finally, we give two examples and numerical simulations to illustrate main results.

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MSC:

92D25 Population dynamics (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34D20 Stability of solutions to ordinary differential equations

Keywords:

stochastic permanence; extinction; Markovian switching; predator-prey model; mutualism
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References:

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