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Title: Modeling and dynamic analysis in a hybrid stochastic bioeconomic system with double time delays and lévy jumps
Authors: Liu, C 
Yu, L
Wang, L
Issue Date: 2018
Publisher: Hindawi
Source: Complexity, 2018, v. 2018, 8294153 How to cite?
Journal: Complexity 
Abstract: A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss asymptotic stability of interior equilibrium. For a stochastic system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis.
ISSN: 1076-2787
EISSN: 1099-0526
DOI: 10.1155/2018/8294153
Rights: Copyright © 2018 Chao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The following publication Chao Liu, Longfei Yu, and Luping Wang, “Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps,” Complexity, vol. 2018, Article ID 8294153, 23 pages, 2018 is available at
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