Bifurcation and optimal harvesting of a diffusive predator-prey system with delays and interval biological parameters.

@article{Zhang2014BifurcationAO,
  title={Bifurcation and optimal harvesting of a diffusive predator-prey system with delays and interval biological parameters.},
  author={Xuebing Zhang and Hongyong Zhao},
  journal={Journal of theoretical biology},
  year={2014},
  volume={363},
  pages={
          390-403
        }
}
This paper deals with a delayed reaction-diffusion three-species Lotka-Volterra model with interval biological parameters and harvesting. Sufficient conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and… Expand
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TLDR
The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations, and this approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Expand
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TLDR
By constructing a suitable Lyapunov functional, a diffusive predator–prey system with discontinuous harvesting function under Neumann boundary conditions is investigated and the existence and some estimates of the positive solution of the system are acquired. Expand
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It is known that one-predator–two-prey system with constant rate harvesting can exhibit very rich dynamics. If such a system contains time delayed component, it can have more interesting behavior. InExpand
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In this paper, we consider the differential-algebraic predator–prey model with predator harvesting and two delays. By using the new normal form of differential-algebraic systems, center manifoldExpand
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Abstract The paper studies the dynamical behaviors of a discrete predator–prey system with nonmonotonic functional response. The local stability of equilibria of the model is obtained. The modelExpand
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Abstract We consider a delayed predator–prey system. We first consider the existence of local Hopf bifurcations, and then derive explicit formulas which enable us to determine the stability and theExpand
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