Competitive Lotka–Volterra population dynamics with jumps

By Jianhai Bao, Xuerong Mao, G. Yin, Chenggui Yuan. 2011

344 citations recorded by the source corpus.

Abstract This paper considers competitive Lotka–Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show that a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the p th moment with p > 0 and reveal the sample Lyapunov exponents; (c) using a variation-of-constants formula for a class of SDEs with jumps, we provide an explicit solution for one-dimensional competitive Lotka–Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our n -dimensional model.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b6beb0e9dd348144523990ea9e5ef9dc69647649

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Ke Wang
2. Meng Liu

In Modeling and Simulation

1. Ke Wang
2. Meng Liu

In Public Health, Environmental and Occupational Health

1. Meng Liu
2. Ke Wang

Citations in the corpus

• Optimal harvesting for a stochastic regime-switching logistic diffusion system with jumps (2014, unknown): “Bao [20] have given an explicit solution for the following logistic population dynamics with jumps: ”
• Coexistence and exclusion of stochastic competitive Lotka–Volterra models (2016, unknown): “in [2] consider competitive system with jumps.”
• Stochastic Lotka–Volterra systems with Lévy noise (2014, background): “that is to say, our conditions are much weaker than that of [3].”
• Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps (2013, background): “[15,16] suggested that these phenomena can be described by a Lévy jump process and they considered stochastic Lotka–Volterra population systems with jumps for the first time.”