Research On Chaotic Neural Networks Based On Delayed Self-feedback

Transient chaotic neural networks are a class of chaotic neural networks used to solve optimization computation problems.Its negative self-feedback term with time decay is introduced on the basis of traditional Hopfield neural network to overcome the defect of being trapped in the minimum and form a chaotic traversal search function.However,the accuracy and speed of the optimization calculation are still unsatisfactory due to the model parameters,annealing strategy,chaotic dynamics and problem complexity.For the above problems,this thesis studies and analyzes the chaotic dynamics characteristics and optimization mechanism of transient chaotic neural networks,and proposes a chaotic neural network model based on delay and self-feedback.The chaotic dynamics of the model is analyzed in detail,and the robustness of the model is investigated and improved.The main research works and innovations of the thesis are:(1)Delayed self-feedback chaotic neural network designDue to the limited global optimization capability of traditional transient chaotic neural networks and the lack of research on delay,this thesis proposes a new chaotic neural network model based on delayed self-feedback,i.e.,introducing delay in the self-feedback term.The Lyapunov exponential and inverse bifurcation diagrams of the chaotic neurons are plotted to analyze their dynamics.In addition,the simulation experiments in which the model is applied to combinatorial optimization and nonlinear function optimization problems show that the delayed self-feedback chaotic neural network is better than the transient chaotic neural network in terms of global optimization seeking ability.(2)Study on anti-disturbance ability of delayed self-feedback chaotic neural networkIn order to study the anti-perturbation ability of delayed self-feedback chaotic neural networks,a model of delayed self-feedback chaotic neuron with perturbation is proposed in this thesis,i.e.,in the internal state of chaotic neuron,a trigonometric function periodic perturbation term and a wavelet function non-periodic perturbation term are introduced,and its dynamics is analyzed on the basis of plotting the inverse bifurcation diagram and Lyapunov exponential diagram.The new transient chaotic neural network constructed by this model is applied to the function optimization and combinatorial optimization problems with different perturbation coefficients selected,and it is concluded that the network model has better antiturbulence ability and robustness under suitable perturbation coefficients.(3)Hysteresis noise delayed self-feedback chaotic neural network designTo address the problem of delayed self-feedback chaotic neural networks under high noise conditions and the accuracy limitation due to premature maturation,hysteresis dynamics is introduced into the internal state equation of chaotic neurons of delayed self-feedback chaotic neural networks,and a delayed self-feedback chaotic neural network with hysteresis noise is proposed.By analyzing and comparing the dynamics of the noise-delayed self-feedback chaotic neural network model with clockwise and counterclockwise hysteresis loops,it can be seen that the model can effectively reduce and mitigate the adverse effects caused by high noise,as well as the random walking ability of random noise can obviously be maintained.Meanwhile,the jump characteristic introduced by the hysteresis loop allows the model to jump out of the minimum at the late stage of convergence.The correctness of the above conclusions is demonstrated by simulation experiments of the combined optimization problem,which show that the hysteresis-noise delayed self-feedback chaotic neural network has better optimization capability compared with other optimization algorithms.