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Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps

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  • Liu, Chao
  • Xun, Xinying
  • Zhang, Guilai
  • Li, Yuanke

Abstract

In this paper, a hybrid stochastic prey–predator system with double time delays and commercial exploitation is established, where combined dynamic effects of telephone noise and Lévy jumps on stochastic population dynamics are taken into accounts. Existence and uniqueness of globally positive solution to the proposed system are investigated. By constructing appropriate stochastic Lyapunov functions, existence of an ergodic and unique stationary distribution of the positive solution is discussed. Sufficient conditions for permanence in mean and extinction of corresponding population are derived. Furthermore, sufficient and necessary criteria for optimal exploitation strategy are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

Suggested Citation

  • Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317224
    DOI: 10.1016/j.physa.2019.123049
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