具有L´evy跳跃的随机控制Lotka-Volterra三种群模型的强收敛性

Q3 Physics and Astronomy

Cybernetics and Physics Pub Date : 2022-12-30 DOI:10.35470/2226-4116-2022-11-4-227-233

C. Romero-Meléndez, D. Castillo-Fernández

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引用次数: 1

摘要

本文研究了受控随机Lotka-Volterra一捕食者-两猎物模型数值解的两个性质，即数值解均值的有界性和这些解的强收敛性。我们还利用随机极大值原理，在具有两种类型的随机环境波动的Lotka-Volterra系统建模的群体中建立并求解相应的最优控制问题：白噪声和L´evy跳跃。我们的研究表明，假设漂移系数和扩散系数的标准线性增长和Lipschitz条件，在这个随机模型中保持了数值解的有界性和格式的强收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strong convergence on a stochastic controlled Lotka-Volterra 3-species model with L´evy jumps

In this paper we study two properties of the numerical solutions of a controlled stochastic Lotka-Volterra one-predator-two-prey model, namely the boundedness in the mean of the numerical solutions and the strong convergence of these solutions. We also establish and solve, by means of the Stochastic Maximum Principle, the corresponding optimal control problem in a population modeled by a Lotka-Volterra system with two types of stochastic environmental fluctuations: white noise and L´evy jumps. Our study shows, assuming standard linear growth and Lipschitz conditions on the drift and diffusion coefficients, that the boundedness of the numerical solutions and the strong convergence of the scheme are preserved in this stochastic model.

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来源期刊

Cybernetics and Physics Chemical Engineering-Fluid Flow and Transfer Processes

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： The scope of the journal includes: -Nonlinear dynamics and control -Complexity and self-organization -Control of oscillations -Control of chaos and bifurcations -Control in thermodynamics -Control of flows and turbulence -Information Physics -Cyber-physical systems -Modeling and identification of physical systems -Quantum information and control -Analysis and control of complex networks -Synchronization of systems and networks -Control of mechanical and micromechanical systems -Dynamics and control of plasma, beams, lasers, nanostructures -Applications of cybernetic methods in chemistry, biology, other natural sciences The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.