We develop a framework for the study of delayed neural fields equations and prove a center manifold theorem for these equations. Specific properties of delayed neural fields equations make it impossible to apply existing methods from the literature concerning center manifold results for functional differential equations. Our approach for the proof of the center manifold theorem uses the origina...

Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y∂x−λz∂z for some λ≠0. The restriction of to Center Manifold has nilpotent origin. We prove if restricted system analytic and center origin, with Andreev number 2, then admits formal inverse Jacobi multiplier. also centers systems, on manifolds, are limits Hopf-type cent...

This paper considers the stabilization problem of nonlinear systems with center manifold (center systems). A new method based on (system) immersion and (manifold) invariance (I&I) is introduced to stabilize the center systems. One of the key steps is to define a target dynamics whose order should be strictly smaller than that of the system to be controlled. For the center systems, we prove that...

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...

This paper addresses the problem of the local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics. A new technique, namely, the Lyapunov function with homogeneous derivative along solution curves has been developed to test the approximate stability of the dynamics on the center manifold. A set of convenient sufficient conditions are provided to test ...

We use center manifold theory to analyze a model of gene transcription and protein synthesis which consists of an ordinary differential equation (ODE) coupled to a delay differential equation (DDE). The analysis involves reformulating the problem as an operator differential equation which acts on function space, with the result that an infinite dimensional system is reduced to one of two dimens...

In a recent paper, we studied bifurcation phenomena in continuous time macroeconometric models. The objective was to explore the relevancy of Grandmont's (1985) ndings to models permitting more reasonable elasticities than were possible in Grandmont's Cobb Douglas overlapping generations model. Another objective was to explore the relevancy of his ndings to a model in which some solution paths ...