Wavelet Chaotic Neural Network with Function Disturbance and Its Application

Chaotic Neural Network has the dynamics property of gradient descent and chaotic at the same time by introducing self-feedback item and simulated annealing strategy. The trigonometric function disturbance was introduced into chaotic neural network and chaotic neural units with function disturbance were studied. The reversed bifurcation and the maximum Lyapunov exponent were given and the dynamic system was analyzed. Energy function was constructed by applying the unified framework theory and was proven to be asymptotically stable. The wavelet chaotic neural network was applied in the function and combinatorial optimization problems. The simulation results show that the chaotic neural network with disturbance of trigonometric function can solve function and combinatorial optimization problems effectively.

I. Introduction

Chaotic neural network's structure is similar to that of Hopfield neural network, and it has transient chaotic response. By combining chaotic dynamics and converging dynamics together, the neural network transit gradually to Hopfield neural network is made. By introducing converging factor, the aim of controlling chaos is attained. Unlike the gradient descent neural network, chaotic neural network has more complex dynamics property, and diversified attractor exists. It is just the dynamics that make it possible for the network to be a technology with abroad application foreground for information processing and optimization computation. [1]–[10]. Chen and Aihara have proposed a CNN with CSA by introducing a linear self-feedback into HNN and reducing the self-feedback connection weight exponentially which ensures that has transient chaotic search behavior and can converge to a point steadily [1]. Chen and Aihara prove that the proposed model is asymptotical stability. Yang proposed a delayed chaotic neural network with annealing controlling strategies to solve the NP-complete maximum clique problem (MCP)[2]. Sun et al. studied a novel hysteretic noisy chaotic neural network for broadcast scheduling problems in packet radio networks and exhibited a stochastic chaotic simulated annealing algorithm [7].