Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model

Abstract This work is concerned with a Holling–Tanner prey–predator model with diffusion subject to the homogeneous Neumann boundary condition. We will obtain some results for the global stability of the unique positive equilibrium of this model, and thus improve some previous results.

[1]  C. S. Holling The functional response of invertebrate predators to prey density , 1966 .

[2]  PETER A. BRAZA,et al.  The Bifurcation Structure of the Holling--Tanner Model for Predator-Prey Interactions Using Two-Timing , 2003, SIAM J. Appl. Math..

[3]  James T. Tanner,et al.  THE STABILITY AND THE INTRINSIC GROWTH RATES OF PREY AND PREDATOR POPULATIONS , 1975 .

[4]  Robert M. May,et al.  Limit Cycles in Predator-Prey Communities , 1972, Science.

[5]  M. Hassell The dynamics of arthropod predator-prey systems. , 1979, Monographs in population biology.

[6]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[7]  Jesse A. Logan,et al.  Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit trees , 1988 .

[8]  Mingxin Wang,et al.  Non-constant positive steady states of the Sel'kov model ☆ , 2003 .

[9]  Eduardo Sáez,et al.  Dynamics of a Predator-Prey Model , 1999, SIAM J. Appl. Math..

[10]  John B. Collings,et al.  Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge , 1995 .

[11]  Rui Peng,et al.  Positive steady states of the Holling–Tanner prey–predator model with diffusion , 2005, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[12]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Sze-Bi Hsu,et al.  Global Stability for a Class of Predator-Prey Systems , 1995, SIAM J. Appl. Math..

[14]  Daniel B. Henry Geometric Theory of Semilinear Parabolic Equations , 1989 .