The purpose of this paper is to study a class of differential]difference equations with two delays. First, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. General stability criteria involving the delays and the parameters are obtained. Second, by choosing one of the delays as a bifurcation...

We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.

This paper is concerned with the asymptotic behavior of solutions to an outflow problem for one-dimensional bipolar quantum Navier-Stokes-Poisson equations in half space. First, by means manifold theory and center theorem, we show existence spatial decay rate stationary solution provided boundary strength small enough. Next, based on elaborate energy estimates, prove that asymptotically stable ...

The Glazman-Povzner-Wienholtz theorem states that the completeness of a manifold, when combined with semiboundedness Schr\"odinger operator $-\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its essential self-adjointness. Our aim is to extend this result operators graphs. We first obtain corresponding for metric graphs, allowing in particular distributional potentials $...

{ Bifurcation analysis provides a methodology for the study of the changes of stability behavior of nonlinear and parameter dependent systems. The inception of bifurcations is associated with systems exhibiting critical modes. Consequently, stabilization of critical systems can be considered as control of the underlying bifurcations. Based on bifurcation equations and the center manifold theore...

In this paper, the bifurcation analysis for Burgers mapping has been studied. The existence and stability of the fixed points of this map was derived. The conditions of existence for pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. The control of the map around stable NeimarkSacker bifurcation has been ac...

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...

Abstract: This paper is concerned with a two species Leslie-Gower predator-prey system with time delay. By regarding the delay τ as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are determined by applying the norm form theory and the cent...

This paper presents the stability and bifurcation analysis of a dynamical model of the heartbeat with time delay. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determinated by applying the center m...

A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory of competitive s...