Synchronization Of Two Classes Of Delayed Complex-valued Chaotical Systems

This thesis concerns the problem of finite-time synchronization for two classes of complex-valued chaotic systems with time-delays.One is finite-time synchronization of coupled complex systems with complex variables and uncertain perturbations.The other is finite-time synchronization of complex-valued neural networks(CVNNs)with mixed delays(time-varying and infinite-time distributed delays)and nonlinear disturbance.When these two kind of systems are considered,the problem of synchronization for complexvalued networks can be effectively solved by decomposing complex variables into real and imaginary parts.In the complex-valued system with coupling delays and disturbances,a simple state feedback controller is designed for achieving finite-time synchronization.Based on Lyapunov theory,a new Lyapunov-Krasovskii function is constructed.According to some inequalities and analysis technologies,it can be easily proved that the complex-valued system with coupling delays and perturbations can achieve finite-time synchronization.Then,a numerical simulation demonstrate the rationality of the theoretical result.Both the driving and response CVNNs are disturbed by external uncertain perturbations,which may be nonidentical.A new state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time.Several sufficient conditions are derived to ensure the synchronization by using inequality techniques and constructing some new Lyapunov–Krasovskii functionals.It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinitetime distributed delays,while it can be explicitly estimated for the CVNNs with bounded delays.Finally,numerical simulations demonstrate the effectiveness of the theoretical results.