一类具有反三角函数自反馈的混沌神经网络及其应用

A Class of Chaotic Neural Networks with Antitrigonometric Function Self-Feedback and Their Applications

在线性自反馈的基础上将反三角函数引入到混沌神经网络的自反馈项,提出了非线性自反馈混沌神经网络模型.网络优化机制的分析表明,非线性自反馈使网络以线性函数与反正切函数的和与状态乘积和的方式影响原Hopfield网络的能量函数,避免网络陷入局部极小点.构造了网络的能量函数,分析了网络达到渐进稳定的充分条件并利用其指导网络求解旅行商问题的参数设置.连续函数优化问题和旅行商问题的仿真研究表明,提出的网络能有效地找到优化问题的最优解.

A Chaotic neural network model with nonlinear self-feedback is proposed by introducing antitrigonometric function into self-feedback of chaotic neural network in the basic of linear self-feedback.The analyses of the optimization mechanism of the networks suggest that nonlinear self-feedback affects the original Hopfield energy function in the manner of the sum of the multiplications of both linear function and antitrigonometric function to the state,avoiding the network being trapped into the local minima.The energy function is constructed,and the sufficient condition for the networks to reach asymptotical stability is analyzed and is used to instruct the parameter set of the networks for solving traveling salesman problem（TSP）.Simulation research on functions＇ optimization and TSP indicates that the proposed networks can find the optimal solution of combinatorial optimization problems.