Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/8294153 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564830050975744 |
|---|---|
| author | Chao Liu Longfei Yu Luping Wang |
| author_facet | Chao Liu Longfei Yu Luping Wang |
| author_sort | Chao Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-89167e97d655475784ad5b2c72410e3d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-89167e97d655475784ad5b2c72410e3d2025-02-03T01:10:11ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/82941538294153Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy JumpsChao Liu0Longfei Yu1Luping Wang2Institute of Systems Science, Northeastern University, Shenyang, ChinaInstitute of Systems Science, Northeastern University, Shenyang, ChinaInstitute of Systems Science, Northeastern University, Shenyang, ChinaA 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.http://dx.doi.org/10.1155/2018/8294153 |
| spellingShingle | Chao Liu Longfei Yu Luping Wang Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps Complexity |
| title | Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps |
| title_full | Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps |
| title_fullStr | Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps |
| title_full_unstemmed | Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps |
| title_short | Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps |
| title_sort | modeling and dynamic analysis in a hybrid stochastic bioeconomic system with double time delays and levy jumps |
| url | http://dx.doi.org/10.1155/2018/8294153 |
| work_keys_str_mv | AT chaoliu modelinganddynamicanalysisinahybridstochasticbioeconomicsystemwithdoubletimedelaysandlevyjumps AT longfeiyu modelinganddynamicanalysisinahybridstochasticbioeconomicsystemwithdoubletimedelaysandlevyjumps AT lupingwang modelinganddynamicanalysisinahybridstochasticbioeconomicsystemwithdoubletimedelaysandlevyjumps |