Permanence and global attractivity of a discrete two-prey one-predator model with infinite delay.
Permanence and global exponential stability of Nicholson-type delay systems
We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
Permanence and positive periodic solutions of a discrete delay competitive system.
Permanence and stability of an age-structured prey-predator system with delays.
Permanence for a delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term
We study a generalized Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we employ a novel proof to establish some criteria guaranteeing the permanence of this model. Moreover, we give an example to illustrate our main result.
Persistence and extinction of a stochastic delay predator-prey model under regime switching
The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.
Persistence and stability for a generalized Leslie-Gower model with stage structure and dispersal.
Positive almost periodic solutions of non-autonomous delay competitive systems with weak allee effect.
Positive periodic solutions for an impulsive ratio-dependent predator-prey system with delays.
Positive periodic solutions of a discrete mutualism model with time delays.
Pseudo almost-periodic solution of shunting inhibitory cellular neural networks with delay.
Qualitative properties of a predator-prey model with delay.
Stability analysis of a delayed SIR epidemic model with stage structure and nonlinear incidence.
Stability and bifurcation in a delayed predator-prey system with stage structure and functional response.
Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay.
Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays
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 Hopf bifurcation in a haematopoietic stem cells model.
Stability switches for some class of delayed population models
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.
The difference equation related to the problem of the hydrogen atom in a strong magnetic field.
The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response
We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some...