Circuit Simulation And Control Of A New Fractional-order Chaotic System

A chaotic system is a nonlinear deterministic system, so the chaotic signal has many nature of random signal, however the chaotic signal is the definite signal. Its prominent characteristic is the sensitive dependence on initial conditions, the boundness and the within randomness. The chaotic signal is particularity between the random signal and the common definite signal. In recent years, the chaotic research has from the pure physics and mathematics theory research to move towards the various applications. At present, the chaos become research hotspots in control, measure and communication security, radar and signal processing, etc. Due to the application of the chaos without the chaotic system design, thus the chaotic system design, control and synchronization has become a very important research subject in the chaos field.The fractional-order calculus theory has 300 years history, but due to long time no actual application background, it developed very slow. Recent years, people found that when the order number of the chaotic system is fractional, the system is still chaotic. The fractional-order calculus operator can accurately described practical dynamic properties of the chaotic systems. Henceforth the fractional-order chaotic system and its application aroused further research.A new fractional-order chaotic system is presented in this paper, some dynamical properties of the system are investigated, the fractional-order chaotic system control and synchronization are researched. Using theoretical analysis, numerical simulations and circuit simulation methods, the problems of the new fractional-order chaotic system design, control and different structure synchronization are solved, and obtained the research results, as follows:A new fractional-order four-dimensional hyperchaotic system is presented, Some dynamical properties of the system are investigated, include the properties of the equilibrium points, scattering character, Lyapunov exponent, Lyapunov dimension, the spectrum of the system and so on. The numerical simulation of this new system is simulated using preliminary estimate and correction difference method. The results prove that chaos actually exists in the system with order as low as 3.2. The circuit of this new system is designed and simulated using Multisim. The results show the chaotic attractor phase diagram and the time domain waveform. Through theoretical analysis, numerical simulation and circuit simulation, the results prove that this new system is chaotic.Based on the fractional-order system stability theory, a simple linear feedback controller is designed, and control this system to equilibrium point. Through theoretical analysis, numerical simulation and circuit simulation, the results are presented to demonstrate the effectiveness of the method.A new fractional-order three-dimensional chaotic system is presented. Some dynamical properties of the system are investigated. The simulation results prove that chaos actually exists with the order as low as 2.34. Based on active control, a synchronization controller between different fractional-order chaotic systems is designed, and the circuit simulation is presented to demonstrate the effectiveness of the method.