Chaos Synchronization Of A Class Of Nonlinear Schrodinger Equation With Periodic Perturbation

In this paper,the chaos synchronization based on a class of nonlinear Schr?dinger equation is studied by nonlinear dynamics method.By theoretical analysis and Melnikov method,we investigated the existence condition of chaos in a class of nonlinear Schr?dinger equation with periodic perturbation and then numerical verification.The different system parameters are selected in order to study the influence of different parameters on the secure communication based on chaos synchronization by numerical simulation.Firstly,the optical soliton and the rogue wave propagation are analyzed and simulated in the perturbation nonlinear system.However,the rogue wave pulse can restore its waveform and continue to spread until it disappears.In view of the fact that the nonlinear dynamical system is prone to chaos and is manipulative to chaos,this paper further discuss the generation of chaos and design chaos synchronization to realize the optical fiber secure communication modeled by Schr?dinger equation.Secondly,we study the optical fiber secure communication modeled by the perturbed Schr?dinger equation.The chaotic signal can be generated from the soliton by a perturbed Schr?dinger equation with multiple frequencies.Theoretical analysis and numerical simulation show that the generation of chaos has nothing to do with the multiplicity.Chaos synchronization can be obtained by feedback control.The speed of synchronization can be expressed by the parameters of the nonlinear Schr?dinger equation.From the Lyapunov stability theory,the synchronization error can be expressed by a nonlinear matrix inequality.Finally,the paper studied the influence of external environment and system parameters on optical secure communication.When the soliton signal is externally disturbed,the chaotic signal can be easily generated.Even if there are some differences between the derived system and the original system,chaos synchronization can be achieved.Results show that smaller differences can lead to faster synchronization.Through this part we can also obtain,change the system parameters can affect the speed of chaos synchronization,the appropriate parametersto accelerate chaos synchronization has an important role.The sixth part is the summary and prospect.