38 research outputs found
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
A boundary value problem in an angle for a second-order parabolic equation of general type
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