Chaotic Neural Networks Based On Wavelet And Hysteresis And Their Applications

Based on connection mechanism, a neural network is composed of neurons according certain connection rule. Compared with the current computer, neural networks are more close to the information processing mode of human brain. Nowadays, neural networks have been powerful tools to solve many problems, and paly important roles in breakthroughing the bottleneck of technology in existence and exploring nonlinearly complex phenomena more deeply.Hopfield neural network is a kind of feedback network. Hopfield neural network receives extensive attention and research because of its successful use in combinatorial optimization problems. However, Hopfield neural network adopts gradient descent mechanism, which enables the network easily trapped into local minima and restricts the applications of the network in complex optimization problems. Enlightened by biologic neuron, researchers introduce chaotic and hysteretic dynamics into Hopfield neural network and propose various improved models. Thereinto, chaotic neural network has more abundant and far-from equilibrium dynamics with various coexisting attractors, and is considered to be the intelligent information processing system which can realize computation in the real world.Although chaotic neural networks improve the optimization performance of Hopfield neural network, they have some deficiencies in solving larger scale of complex combinatorial optimization problems. Based on the forward research, this thesis organically combines chaotic neural networks with hysteretic dynamics and wavelet technology. The main works and results are as follows:Firstly, wavelet technology is reasonably introduced into chaotic neural networks, and a new chaotic neural network model is present, which realize the organic combination of the chaotic neural network and wavelet technology and sufficiently paly the role of wavelet technology in chaotic ergodicity search. Based on the above, the chaotic dynamic property and the unique fixed point of the wavelet chaotic neuron are analyzed, which suggests that the wavelet chaotic neuron has chaotic searching ability and can converge stably. The additional energy modifier, which can enable the chaotic traverse of the network to exhibit local and detailed searching characteristics, is studied. And the validity of the additional energy modifier is verified by simulations. In addition, the energy function of the wavelet chaotic neural network is provided, and the asymptotical stability of the network using Lyapunov stability approach is proven, and the sufficient condition of stability is provided. In the last, the simulations in traveling salesman problems testify the optimization performance of the wavelet chaotic neural network.Secondly, the concrete expression of Gauss wavelet scale annealing and the effect of Gauss wavelet scale annealing on the chaotic ergodicity search of the hysteretic chaotic neural network are further studied. Lyapunov exponent, which can reflect dynamic level of systems, is used to show the abundant dynamic characteristics of Gauss wavelet scale annealing. Analyses show that the hysteretic chaotic neural network based on scale annealing can also achieve stability. In the last, the hysteretic chaotic neural network with Gauss wavelet scale annealing is applied to realize CDMA multi-user detector and weaken the multi-access interference of CDMA systems.Finally, in order to improve the optimization performance of noisy chaotic neural network with higher noise levels under the condition of not introducing any extra system parameters, this thesis first transforms the original noisy chaotic neural network into an equivalent network model, and then proposes a hysteretic noisy chaotic neural network by controlling the noise in the equivalent model to exhibit hysteretic dynamics and stochastic chaotic simulated annealing property simultaneously. During the process, this thesis analyzes two nural models equivalent to the noisy chaotic neuron, and selects one of them that can be realized in physics to construct the hysteretic noisy chaotic neural network. Compared with the original noisy chaotic neural network, the proposed hysteretic noisy chaotic neural network can suppress noises by hysteretic dynamics and improve the optimization performance with higher noise levels. Simulations in the broadcast scheduling of packet radio networks and multi-targets tracking in the environment of dense clutters testify the optimization performance of the proposed hysteretic noisy chaotic neural network.