Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species
Autor: | Hai-Feng Huo, Ni-Ni Qin, Xin-You Meng |
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Rok vydání: | 2018 |
Předmět: |
01 natural sciences
Stability (probability) Models Biological Pontryagin's minimum principle Predation symbols.namesake Maximum principle predator–prey Species Specificity 0103 physical sciences Normal form theory Applied mathematics Quantitative Biology::Populations and Evolution Animals Computer Simulation Disease 0101 mathematics 010301 acoustics lcsh:QH301-705.5 Ecology Evolution Behavior and Systematics lcsh:Environmental sciences Mathematics Hopf bifurcation lcsh:GE1-350 Ecology optimal harvesting policy 010102 general mathematics Dynamics (mechanics) Characteristic equation Numerical Analysis Computer-Assisted time delay lcsh:Biology (General) Predatory Behavior symbols hopf bifurcation |
Zdroj: | Journal of Biological Dynamics, Vol 12, Iss 1, Pp 342-374 (2018) |
ISSN: | 1751-3766 |
Popis: | In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results. |
Databáze: | OpenAIRE |
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