### Mathematical Biosciences and Engineering

2019, Issue 4: 2717-2737. doi: 10.3934/mbe.2019135
Research article Special Issues

# The survival analysis of a stochastic Lotka-Volterra competition model with a coexistence equilibrium

• Received: 01 January 2019 Accepted: 17 March 2019 Published: 27 March 2019
• In this paper, we propose and analyze a two-species Lotka-Volterra competition model with random perturbations that relate to the inter-specific competition rates and the coexistence equilibrium of the corresponding deterministic system. The stochasticity in inter-specific competition (between species) is more important than that in intra-specific competition (within species). We pose two assumptions and then obtain su cient conditions for coexistence and for competitive exclusion respectively, and find that small random perturbations will not destroy the dynamic behaviors of the corresponding deterministic system. Moreover, if one species goes extinct, the convergence rate to zero is obtained by investigating the Lyapunov exponent. Finally, we provide several numerical examples to illustrate our mathematical results.

Citation: Junjing Xiong, Xiong Li, Hao Wang. The survival analysis of a stochastic Lotka-Volterra competition model with a coexistence equilibrium[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2717-2737. doi: 10.3934/mbe.2019135

### Related Papers:

• In this paper, we propose and analyze a two-species Lotka-Volterra competition model with random perturbations that relate to the inter-specific competition rates and the coexistence equilibrium of the corresponding deterministic system. The stochasticity in inter-specific competition (between species) is more important than that in intra-specific competition (within species). We pose two assumptions and then obtain su cient conditions for coexistence and for competitive exclusion respectively, and find that small random perturbations will not destroy the dynamic behaviors of the corresponding deterministic system. Moreover, if one species goes extinct, the convergence rate to zero is obtained by investigating the Lyapunov exponent. Finally, we provide several numerical examples to illustrate our mathematical results.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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