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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Changjin Xu, Maoxin Liao, Xiaofei He (2011)

International Journal of Applied Mathematics and Computer Science

In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations...

Stability and optimal harvesting of a prey-predator model with stage structure for predator

Tapan Kumar Kar (2005)

Applicationes Mathematicae

The dynamics of a prey-predator system, where predator has two stages, a juvenile stage and a mature stage, is modelled by a system of three ordinary differential equations. Stability and permanence of the system are discussed. Furthermore, we consider the harvesting of prey species and obtain the maximum sustainable yield and the optimal harvesting policy.

Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes

Yanling Tian (2014)

Applications of Mathematics

A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification...

Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays

Ramachandran Raja, Rathinasamy Sakthivel, Selvaraj Marshal Anthoni, Hyunsoo Kim (2011)

International Journal of Applied Mathematics and Computer Science

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical...

Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon, H. R. Thieme (2010)

Mathematical Modelling of Natural Phenomena

For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...

Stability of unique pseudo almost periodic solutions with measure

Boulbaba Ghanmi, Mohsen Miraoui (2020)

Applications of Mathematics

By means of the fixed-point methods and the properties of the μ -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the μ -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where μ is a positive measure. A numerical example is given to illustrate our main results.

Stability switches for some class of delayed population models

Joanna Skonieczna, Urszula Foryś (2011)

Applicationes Mathematicae

We study stability switches for some class of delay differential equations with one discrete delay. We describe and use a simple method of checking the change of stability which originally comes from the paper of Cook and Driessche (1986). We explain this method on the examples of three types of prey-predator models with delay and compare the dynamics of these models under increasing delay.

Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems

Sachiko Ishida, Tomomi Yokota (2023)

Archivum Mathematicum

This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.

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