Stability and bifurcation analysis of time delay systems

In this thesis, the analyses of bifurcation and stability and synchronization of some nonlinear time delay systems described by retarded functional differential equations have been aimed to perform via Lambert W function and generalised modified Mikhailov stability criterion. For this purpose, first of all, bifurcation and stability analyses of a nonlinear time delay chaotic system have been achieved for different system parameters. By utilizing the linearized model of the equilibrium points of the system, the presence of bifurcation and bifurcation point have been calculated analytically according to the time delay parameter. The direction of bifurcation has been determined by Lambert W function and generalised modified Mikhailov stability criterion. Secondly, chaos synchronization of two identical chaotic, nonlinear time delay systems (one Master-Transmitter other Slave-Receiver) have been achieved for different initial conditions. For achieving synchronization between two systems, a proportional controller has been designed by using active control method. Efficiency of designed controller has been tested using Lambert W function and generalised modified Mikhailov stability criterion and appropriate gain parameter has been selected. Thirdly, bifurcation and stability analyses of nonlinear one-cell delayed cellular neural network have been achieved for different system parameters. The presence of bifurcation and bifurcation point has been calculated analytically. The direction of bifurcation has been computed by Lambert W function and generalised modified Mikhailov stability criterion. The analytical results have been verified by simulation results obtained from the Matlab/Simulink environment for each three practices. Keywords: Time delay systems, Bifurcation analysis of time delay systems, Stability analysis of time delay systems, Synchronization of time delay systems, Lambert W function, Generalised modified Mikhailov stability criterion.