Research And Application To Chaotic Neural Networks And Their Optimization Algorithm

Chaotic system is a kind of determined system and at the same time it appears random phenomenon which looks like to have no rules. Because of this property, it can be used in each realm of science. Recently people find that the chaos phenomenon exists in human brain, chaotic theory can explain some irregular thing in brain. So chaotic dynamics offers new chance for studying neural network, the research of chaotic neural network(CNN) becomes a new task for us. Unlike the gradient descent neural network, the chaotic neural network has more complex dynamics property, and diversified attractor exists. It is just this dynamics property that make it possible for the network to be a technology with extensively application foreground for information processing and optimality calculation. A in-depth research is done to chaotic neural network in this pape. Firstly, it introduces the basic theories of the chaotic dynamics completely, gives the concept of chaos, the qualitative attribute, the Lyapunov index, the Kolmogorov entropy, and so on. And then it makes two examples, Logistic and Lorenz Equation, which are the most typical chaotic systems, and analyses them in detail. Secondly, it introduces the model of Hopfield neural network(HNN), and uses the model of continuous Hopfield neural network(CHNN) to solve traveling salesman problem(TSP). Thirdly, on the base of HNN, it gets a kind of chaotic neural network algorithm based on annealing strategy(ACNN), and Carries on the research carefully. It introduces chaos mechanism into HNN, and then applies chaotic ergodicity to stochastic search and controls the chaotic dynamics by annealing strategy to perform inverse bifurcation and disappear. ACNN gradually approaches to HNN and converges to a stable point which is globally optimal or near-optimal. Simulation result shows that ACNN is a global optimization algorithm which can effectively avoid local minimal. Lastly, it designs a new improved kind of chaotic neural network algorithm based on annealing strategy(IACNN). Simulation result shows that IACNN has more rapid convergenced speed than ACNN.