Local Analytic Solutions Of Functional Differential Equations With Deviating Arguments Depending On The State Derivative

Nonlinear science is one of the most important topics in today's sciences. The theory of iterative dynamical systems plays an important role in nonlinear science. The study of iterative dynamical systems involves iterative functional differential equations . Ihey are differetial equations with deviating argument of the unknown function ,and the delay function epends not only on the argument of the unknown function ,but also state or state derivative,even higher order derivatives.Such equations are kinds of new functions quite different from the usual differential equations (Retarded FDE ,Neutral FDE , Advanced FDE)which formed a systemic theory[l]Many problems of dynamical systems can be reduced to an iterative functional differential equation.For example, the two-body problem in a classic electrodynamics, some population models, some models of commodity price fluctuations and models of blood cell productions are given in the form of iterative functional differential equations. Therefore ,it is important in study of many domain such as physics ,sybernetics ,chess games , biology. In this paper ,we discuss local analytic solutions of two forms of functional differential equations with deviating arguments depending on the state derivative or secondly derivative.In Chapter 1,concepts, applications and importances of iteration,dynamical system , iterative functional differential equation are introduced. Many known results on iterative functional differential equations arc summarized,and the...