Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps

Li, Wen Rui; Zhang, Qi Min; Meyer‐Baese, Anke; Ye, Ming; Li, Yan

doi:10.3934/mbe.2020145

Mathematical Biosciences and Engineering

2020

DOI: 10.3934/mbe.2020145

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Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps

Wen Rui Li

Qi Min Zhang

Anke Meyer‐Baese

et al.

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Cited by 3 publications

References 25 publications

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A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps

Gao,

2024

era

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<abstract>The Ornstein-Uhlenbeck (OU) process was used to simulate random perturbations in the environment. Considering the influence of telegraph noise and jump noise, a stochastic Gilpin-Ayala nonautonomous competition model driven by the mean-reverting OU process with finite Markov chain and Lévy jumps was established, and the asymptotic behaviors of the stochastic Gilpin-Ayala nonautonomous competition model were studied. First, the existence of the global solution of the stochastic Gilpin-Ayala nonautonomous competition model was proven by the appropriate Lyapunov function. Second, the moment boundedness of the solution of the stochastic Gilpin-Ayala nonautonomous competition model was discussed. Third, the existence of the stationary distribution of the solution of the stochastic Gilpin-Ayala nonautonomous competition model was obtained. Finally, the extinction of the stochastic Gilpin-Ayala nonautonomous competition model was proved. The theoretical results were verified by numerical simulations.</abstract>

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A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps

Gao,

2024

era

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Dynamical behaviors of a Lotka-Volterra competition system with the Ornstein-Uhlenbeck process

Wei¹,

2023

MBE

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<abstract>The competitive relationship is one of the important studies in population ecology. In this paper, we investigate the dynamical behaviors of a two-species Lotka-Volterra competition system in which intrinsic rates of increase are governed by the Ornstein-Uhlenbeck process. First, we prove the existence and uniqueness of the global solution of the model. Second, the extinction of populations is discussed. Moreover, a sufficient condition for the existence of the stationary distribution in the system is obtained, and, further, the formulas for the mean and the covariance of the probability density function of the corresponding linearized system near the equilibrium point are obtained. Finally, numerical simulations are applied to verify the theoretical results.</abstract>

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A stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps

Gao,

2024

MBE

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<abstract>By using the Ornstein-Uhlenbeck (OU) process to simulate random disturbances in the environment, and considering the influence of jump noise, a stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps was established, and the asymptotic behaviors of the stochastic Gilpin-Ayala mutualism model were studied. First, the existence of the global solution of the stochastic Gilpin-Ayala mutualism model is proved by the appropriate Lyapunov function. Second, the moment boundedness of the solution of the stochastic Gilpin-Ayala mutualism model is discussed. Third, the existence of the stationary distribution of the solution of the stochastic Gilpin-Ayala mutualism model is obtained. Finally, the extinction of the stochastic Gilpin-Ayala mutualism model is proved. The theoretical results were verified by numerical simulations.</abstract>

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Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps

Cited by 3 publications

References 25 publications

A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps

A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps

Dynamical behaviors of a Lotka-Volterra competition system with the Ornstein-Uhlenbeck process

A stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps

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