title: Bifurcation and optimal harvesting of a diffusive predator-prey system with delays and interval biological parameters.
abstract: 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 center manifold theorem. Then an optimal control problem has been considered. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical evidence shows that the presence of harvesting can impact the existence of species and over harvesting can result in the extinction of the prey or the predator which is in line with reality.
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People׳s Republic of China; Department of Basic Course, Huaian College of Information Technology, Huaian 223003, People׳s Republic of China.
authors.forename: Xuebing
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People׳s Republic of China. Electronic address: hongyongz@126.com.
authors.forename: Hongyong
authors.initials: H
authors.lastname: Zhao
mesh_terms: D020387:Food Chain; D008954:Models, Biological; D011157:Population Dynamics; D013045:Species Specificity
keywords: Hopf bifurcation; Reaction–diffusion; Stability; Three species