Chaotic Function Projective Synchronization Research Based On Different Schemes

Chaos theory is an important branch of nonlinear science which is a basic science to study the nonlinear phenomena in common. Chaotic secure communication is the most widely used areas in the future, and chaotic synchronization as the foundation of chaotic secure communication has attracted more and more attention. Function projective synchronization (FPS) is a new method of synchronization that has been proposed by scholars recently, compared to the methods talked before, such as completed synchronization, anti-synchronization and projective synchronization etc., which have more evident features and advantages, like the greatly enhanced level of security encryption of information. In this paper, theoretical analysis and numerical simulation experimental methods are combined to study the issues of FPS based on several different synchronization schemes. The main contrubutions of the paper are as follows:Firstly, before doing the research to FPS, projective synchronization has been introduced, which is simpler than FPS. Based on fractional differential principles and fractional stability theory, using pole placement method to design a suitable state observer, and then take the fractional-order cellular neural network chaotic system as an example to study the heterogeneous projective synchronization. Finally, the numerical simulation experiments verify the effectiveness of method.Secondly, because the scaling factor of projective synchronization is a constant, such that synchronization trajectory is just evoluted according to a particular ratio, which will generate security flaw. However, FPS replaces the constant scaling factor to a time proportion function, through choosing different proportion function make the output chaotic signals whose ratio is different from the original drive system. The FPS increases the difficulties of interception of outputting the chaotic signals, which make the chaotic secure communication more secure. Therefore, based on the open-plus-closing-looping (OPCL) coupling method, the paper constructs the corresponding response system of integral-order and fractional-order that we give respectively, and researches FPS of driver-response systems with system parameters perturbation or not. Paper takes Qi chaotic system and four-order hyper-chaotic Lii system as example to study above different conditions. Through the numerical simulations further confirm the effectiveness and robust of the scheme. Simultaneously, the paper uses finite-time and Lyapunov stability theories to study the finite-time FPS of hyper-chaotic Lorenz system combined theoretical analysis with experimental simulation, and the experimental results prove the validity of this scheme.Finally, modified function projective synchronization (MFPS) of a quantum cellular neural network has been researched after FPS. The so-called MFPS is defined as the each proportion of its proportion functions is not the same which further improve the degree of information encryption than FPS. In this paper, combined with the linear separation and pole placement technique to design appropriate state-observer, and use numerical simulation to further determine the feasibility of this method.