𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global asymptotic stability for predator–prey models with environmental time-variations

✍ Scribed by Yasuhisa Saito; Jitsuro Sugie; Yong-Hoon Lee

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
255 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

This paper considers a Lotka-Volterra predator-prey model with predators receiving an environmental time-variation. For such a system, a unique interior equilibrium is shown to be globally asymptotically stable if the time-variation is bounded and weakly integrally positive. Our result tells that the equilibrium can be stabilized even by nonnegative functions that make the limiting system structurally unstable. Numerical simulations are also shown to illustrate the result and to suggest that cases with time-variation acting on predators have larger-scale convergence to the equilibrium than population dynamics with time-variation acting on prey.

📜 SIMILAR VOLUMES

Global asymptotic stability of positive
Global asymptotic stability of positive steady states of a diffusive ratio-dependent prey–predator model
✍ Mingxin Wang; Peter Y.H. Pang 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 223 KB

In this work, we study a ratio-dependent prey-predator model with diffusion and homogeneous Neumann boundary condition. We prove that the unique positive constant steady state is locally and uniformly stable, and is globally asymptotically stable under some assumptions. The proof uses the iteration

Global asymptotic stability for neural n
Global asymptotic stability for neural network models with distributed delays
✍ José J. Oliveira 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 667 KB

In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the non-delayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings,

Global Qualitative Analysis for a Ratio-
Global Qualitative Analysis for a Ratio-Dependent Predator–Prey Model with Delay
✍ Sanyi Tang; Lansun Chen 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 147 KB

A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic st

Global attractor for a three-species pre
Global attractor for a three-species predator-prey model with cross-diffusion
✍ Haojie Guo; Sining Zheng 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 130 KB 👁 1 views

## Abstract This paper studies a three‐species predator‐prey model with cross‐diffusion. In a previous paper 11 of Pang and Wang, it was proved that the system admits global classical solutions if the exponents in cross diffusion term satisfy __m__, __l__ ≥ 1. In the present paper, we continue cons