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...

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given. Keyw...

This book provides a basis for learning the basic principles of applied mathematical sciences, uses bifurcations nonlinear dynamical systems

The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail:...

two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. in this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. an analytical model is developed based on marciniak-kuczynski method associated hill’s non-quadratic yield criterion. formin...