Study On Synchronization Control Of Chaotic And Fractional-order Chaotic Systems With Circuitry Experimental Verification

Chaotic systems are well known for their complex nonlinear systems, and have been intensively studied in various fields such as physics, chemistry, information technology and engineering. In virtue of its characteristics of chaos such as hyper sensitivity to initial conditions, high randomicity and board spectra for its Fourier transform, chaos can be especially applied to secure communications, signal processing and image encryption and so on. Thus chaos synchronization has become the key process in the application of chaos. The research has studied the relative problems of chaos synchronization, synchronization of fractional-order hyper-chaotic systems and analysis of a new four-dimensional non-autonomous hyper-chaotic system, using the methods of theoretical derivation, numerical simulation and circuitry experimental verification. The main contributions of this paper are list as follows:1. Based on Lyapunov stability theory, the nonlinear feedback controller and parameter recognizer were designed with the adaptive control method. The uncertain single-mode laser Lorenz system is taken as the drive system and the uncertain single scroll attractor chaotic system as the response system in the design, which makes all the status variable of the response system to follow the chaotic path of the drive system strictly in function proportion, and recognizes all the uncertain parameters including unknown coefficients of nonlinear terms of the drive and response systems. The result obtained by the four-order Runge-Kutta simulation indicates the effectiveness and feasibility of the method.2. Three different synchronization schemes based on the Pecora-Carroll principle, the linearization by feedback and back-stepping approach based on Lyapunov equation are proposed to realize chaotic synchronization. Some methods such as linearization feedback control method eliminate nonlinear terms of systems when designing controllers, which make the coefficient matrix of the system to be the constant matrix. Although these schemes can control the fractional-order chaotic system to synchronize, it costs too much. And then, based on fractional stability theory, the adaptive control method proposed in this paper can achieve synchronization of fractional-order hyper-chaotic systems only using two controllers, and adaptive controller and updating law of parameter are obtained. Numerical simulations confirm the effectiveness of the proposed synchronization approaches. Especially, the circuit experiment simulations also demonstrate that the experimental results are in agreement with numerical simulations. Moreover, the active control technique is applied to synchronize the different fractional-order hyper-chaotic systems, numerical simulations have performed the effectiveness and feasibility of the presented synchronization techniques.3. A new four-dimensional non-autonomous hyper-chaotic system is presented by adding input sine signal to a hyper-chaotic system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyper-chaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the non-autonomous system are analyzed. Also, the synchronizing circuits of the non-autonomous hyper-chaotic system are designed via the synchronization control method of single variable coupling feedback. The electronic circuits are implemented and the experimental results observed by the oscillograph well agreed with the simulation results.