Periodic solutions of logistic equations with time delay

AbstractA new criterion is established for the existence of positive periodic solutions to the following delay logistic equation: u′(t)=u(t)[r(t)−a(t)u(t)+b(t)u(t−τ)] where r(t), a(t), b(t) are periodic continuous functions, a(t)>0, b(t)≥0 and r(t) has positive average

Diffusive Holling–Tanner predator–prey models in periodic environments

In this paper, by using the Lyapunov method, we establish sufficient conditions for the global asymptotic stability of the positive periodic solution to diffusive Holling–Tanner predator–prey models with periodic coefficients and no-flux conditions

Global Stability in competitive periodic systems

A competitive Lotka–Volterra system of two equations is studied. It is shown that if the coefficients are continuous, periodic and satisfy certain average conditions then a positive periodic solution exists which is globally asymptotically stable in R^2+

Some Global Results for the Degn–Harrison System with Diffusion

This paper considers the Degn–Harrison reaction–diffusion system subject to homogeneous Neumann boundary conditions in a smooth and bounded domain. Using the presence of contracting rectangles and the method of Lyapunov, we establish sufficient conditions for the global asymptotic stability of the unique constant steady state