The fundamental theory of existence, uniqueness and continuous differentiability of Lp-solutions for Neutral Functional Differential Equations is presented. Also, the spectrum of the solution operator of general autonomous linear NFDEs is described. Finally, an extension of Hartman Grobman Theorem on local conjugacy near a hyperbolic equilibrium is proved.

The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays...

An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.

This work deals with the analysis pertaining some dynamic behavior of vector solutions of first order two-dimensional neutral delay differential systems of the form $$\frac{\mathrm{d}}{\mathrm{d}t}\left[\begin{array}{c}u\left(t\right)+pu(t-\tau )\\ v\left(t\right)+pv(t-\tau )\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\left[\begin{array}{c}u(t-\alpha )\\ v(t-\beta )\end{array}\right].$$ The effort has been made to study $$\frac{\mathrm{d}}{\mathrm{d}t}\left[\begin{array}{c}x\left(t\right)-p\left(t\right)h_1\left(x(t-\tau )\right)\\ y\left(t\right)-p\left(t\right)h_2\left(y(t-\tau )\right)\end{array}\right]+\left[\begin{array}{cc}a\left(t\right)& b\left(t\right)\\ c\left(t\right)& d\left(t\right)\end{array}\right]\left[\begin{array}{c}{f}_1\left(x(t-\alpha )\right)\\ f_2\left(y(t-\beta )\right)\end{array}\right]=0,$$ where $p,a,b,c,d,h_1,h_2,f_1,f_2\in C(ℝ,ℝ)$; $\alpha ,\beta ,\tau \in {ℝ}^{+}$. We verify our results with the examples.

This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.

In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.

We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent')...

The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve...

Este trabajo tiene como objeto presentar resultados de existencia global de soluciones para ciertas ecuaciones diferenciales funcionales asociadas a procesos con retardo variable. El principal argumento será la aplicación de ciertas estimaciones puntuales sobre las soluciones de una ecuación diferencial escalar.