Stability Analysis Of Some Kinds Of Delay Differential Equation And It’s Application To Chaos Control

Delay differential equations have considerable applications to natural science and social science. The general dynamic systems involve time delays. So delay differential equation can exhibit much more real word phenomena.Stability is preserving theory which solution of equations can preserve little change if differential equations or initial conditions have little change. The solutions happening huge change is no meaning. So, it is meaningful to study stability of differential equation in theory and practice.Chaos phenomenon is a common phenomenon in nonlinear science. The initial conditions have little change can make system happening huge change. Delayed feedback is an important method for controlling chaos.In this paper, stability of differential equations is studied and study chaos of the Hopfield-type neural networks by time-delayed feedback. The thesis mainly works as follows:(1) The delayed Leslie-Gower predator-prey is investigated. By constructing a Lyapunov function, the sufficient conditions for global stability of the positive equilibrium are obtained.(2) Coupled oscillator systems with delayed feedback is considered, when angular frequency is a constant. By employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, stability and the existence of multiple periodic solutions are investigated, some numerical simulations are given.(3) Neural network system with delayed feedback is considered. Model consider time delay factor. The existence of local Hopf bifurcation is discussed. The application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.