| This paper mainly studies the issues in biomedical engineering based on the chaotictheory. It includes the nonlinear dynamical analyses of theαwaves of epileptic EEG(Electroencephalogram) signal, chaotic synchronization of neuron network system and itsapplication in secure communication, tracking control for a class of chaotic systems.Extract theαwaves from the normal, epileptic and resume period of epileptic EEGwith the wavelet decomposition method, and then compute and analyses them according tophase space reconstruct technique from one-dimensional and nonlinear quantitative criterion.The conclusion can be got by the comparison of the phase diagrams, power spectrums andcorrelation dimensions of normal and epilepticαwaves: The phase diagram, powerspectrum and correlation dimension of theαwaves of EEG can change regularly under theinfection of the pathology. They can reflect the health of human. Theαwave of EEG is inchaos under the normal physiological status and is tend to be in order under the epilepticstatus.The problem of chaotic dynamics of third order Winner-Take-All competitive neuronsystem is studied and a method is presented to realize the self synchronization and thedifferent structure synchronization of the system; Based on the principle of stabilizationjudgment of linear systems, a method of projective synchronization is presented to study theproblem of chaotic projective synchronization of fourth order Cellular Neural Networks(CNN) and applied to secure communication. The results of numerical simulations arefurther indications for the feasibility of the method adopted.Take Hindmarsh-Rose neuron system as an example to study the problem of trackingcontrol for a class of chaotic systems. A tracking controller is designed and provedtheoretically that it can make this class of chaotic system track any given signal and realizeself synchronization and different structure synchronization. Numerical simulations show thefeasibility of the method adopted. |
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