Center Manifold Theory for Functional Differential Equations of Mixed Type
نویسنده
چکیده
We study the behaviour of solutions to nonlinear autonomous functional differential equations of mixed type in the neighbourhood of an equilibrium. We show that all solutions that remain sufficiently close to an equilibrium can be captured on a finite dimensional invariant center manifold, that inherits the smoothness of the nonlinearity. In addition, we provide a Hopf bifurcation theorem for such equations. We illustrate the application range of our results by discussing an economic life-cycle model that gives rise to functional differential equations of mixed type.
منابع مشابه
Fractional dynamical systems: A fresh view on the local qualitative theorems
The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...
متن کاملEquivariant Hopf bifurcation for functional differential equations of mixed type
In this paper we employ the Lyapunov–Schmidt procedure to set up equivariant Hopf bifurcation theory of functional differential equations of mixed type. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction. © 2010 Elsevier Ltd. All rights reserved.
متن کاملBifurcation Theory of Functional Differential Equations: a Survey∗
In this paper we survey the topic of bifurcation theory of functional differential equations. We begin with a brief discussion of the position of bifurcation and functional differential equations in dynamical systems. We follow with a survey of the state of the art on the bifurcation theory of functional differential equations, including results on Hopf bifurcation, center manifold theory, norm...
متن کاملA Center Manifold Result for Delayed Neural Fields Equations
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...
متن کاملRandom fractional functional differential equations
In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.
متن کامل