Hyperchaotic System And Its Synchronization Research With Different Structure

Chaotic systems have shown a non-periodic behaviors which exist in deterministicnonlinear dynamic systems. It has some features such as high randomicity, broadbandspectrum and property of sensitive dependence on initial conditions. Chaoticsynchronization is one of the key technologies applied in biology, secure communicationand information science and other fields have broad application prospects.Since the1990s, chaotic synchronization has been one of the hot topics.Hyperchaotic system has more complex dynamic behaviors, secure communication withhyperchaotic system has better crack resistance ability of the information. Two identicalsystems are difficult to obtain in the actual problem，the research on synchronization withdifferent structure systems has practical significance. Fractional-order chaotic systemsare the promotion of the integer-order chaotic systems and they have with more complexdynamics. First of all, synchronization of fractional-order chaotic systems to help peoplerecognize the nature and development of the basic law of nature; Secondly, it provides acertain degree of universality for the applications of fractional-order hyperchaotic systemin the field of chaotic secure communication. Therefore, this topic is mainly to carry outas follows:(1) Synchronous of hyperchaotic system based on inverse system designThe research design hyperchaotic synchronization method based on inverse system.This method start from the error function of hyperchaotic synchronization system,according to the model of Lie out the derivative of the system to determine the relativeorder inverse system, and then through the linear system comprehensive design methoddesign the controller. The control simulation example shows the feasibility and validityof the method. The results for the synchronization of hyperchaotic system improve themethod to the solution of the problem for reference.(2) Rucklidge hyperchaotic system and its function projective synchronization withdifferent hyperchaotic systemA4D Rucklidge hyperchaotic system is proposed in this paper. The nonlineardynamical properties of the system are analyzed. Both the circuit realization of thehyper-chaotic system and Multisim simulation results are presented. Based on theLyapunov stability theory, an adaptive control method with corresponding parametersupdate rule is designed for achieving adaptive generalized function projectivesynchronization between two diverse hyper-chaotic systems. Synchronization of thepresented system and Chen hyper-chaotic system is considered as typical example, and the numerical results verify the validity and feasibility of the synchronization method.(3) Synchronization of fractional-order hyperchaotic RucklidgeBased on the stability theory of fractional-order linear systems, a new controllerwith active control strategy is deduced from the dynamical equations of thefractional-order hyperchaotic systems, which is used for realizing the generalizedprojective synchronization of two different hyperchaotic systems. The generalizedprojective synchronization between the fractional-order hyperchaotic Chen system andthe fractional-order hyperchaotic Lorenz system、 the fractional-order hyperchaoticRucklidge system and the fractional-order hyperchaotic Chen system are considered asan example. Numerical results are performed to verify the effectiveness and feasibility ofthe presented synchronization scheme.