A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The directi...

In this paper, by using the Hopf’s bifurcation theorem we will discuss the existence of small amplitude periodic solutions of the equation ẍ(t)+ f(x(t))ẋ(t) + g(x(t − r)) = 0, taking as bifurcation parameter c either d or r. We assume that r > 0, f ∈ C, f(0) = c > 0, g(0) = 0 and ġ(0) = d > 0.

An epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the ...

We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the normal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determin...

and Applied Analysis 3 Substituting τ = τ j and λ = iω 0 into (17), we obtain