A New Fractional Order Hyper-chaotic System Design And Its Control Circuit Simulation

Fractional order chaotic systems is generalized in the form of an integer-order chaoticsystems, but it is more complex physical characteristics than integer-order chaotic systems,which is widely used in physics and many engineering fields. In recent years, the research offractional chaotic synchronization and control. It also demonstrates the broader applicationprospects.Through the software and the circuit simulation software, designing a new fractionalhyper-chaotic system was based on the integer-order hyper-chaotic systems on the throughsoftware and circuit simulation software. The main content was as follows:(1) Through the feedback system designed to extend the high-dimensional hyper-chaoticsystem to meet two or more positive Lyapunov exponent, the system tracks the phase diagramof the separation space in multiple directions, so that the new system has a more complexdynamic learning behavior. By the definition of chaos, Poincare section method, Lyapunovexponent, Lyapunov functions, etc., to analyze the characteristics of nonlinear dynamics andits associated physical properties.(2) The nature of fractional calculus, Grunwald-Lemikov (GL) is defined, Gammafunction and its reciprocal function, designed a four-dimensional hyper-chaotic system,through a large numerical simulations showed that: when q=0.80~0.99chaotic phenomenaoccur, and analysis of its equilibrium, stability, Lyapunov exponent and other relevantcharacteristics.(3) Fractional synchronization control structure in a new four-dimensional theory offractional hyper-chaotic system trajectory tree unit circuit, the dynamic observation variablesin the phase diagram Multsim circuit simulation platform, through the process of renderingand simulation results are compared circuit implementation, found that the system has anearly identical chaotic attractor phase diagram. Chaos synchronization of the control systemby the tracking control theory, design a simple and effective linear feedback trackingcontroller, two closed track switch synchronous controller waveforms observed before andafter the closed system of equations, clearly see the actual effect of the feedback trackingcontroller...