Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays

Periodic and Homoclinic Solutions of Extended Fisher-Kolmogorov Equations

In this paper we study the existence of periodic solutions of the fourth-order equations u − pu′′ − a x u + b x u3 = 0 and u − pu′′ + a x u − b x u3 = 0, where p is a positive constant, and a x and b x are continuous positive 2Lperiodic functions. The boundary value problems P1 and P2 for these equations are considered respectively with the boundary conditions u 0 = u L = u′′ 0 = u′′ L = 0. Exi...

Spatial Patterns Described by the Extended Fisher-kolmogorov (efk) Equation: Periodic Solutions

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the R(n)(+)-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-V...

Positive Periodic Solutions of Neutral Logistic Equations with Distributed Delays

Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t) h a(t)− n X i=1 ai(t) Z 0 −Ti x(t+θ) dμi(θ)− m X j=1 bj(t) Z 0 −T̂j x′(t+θ) dνj(θ) i , where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The value...

Asymptotic behavior of solutions for a class of predator – prey reaction – diffusion systems with time delays ✩

The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator–prey reaction–diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state ...