Abstract: As to the monotonous activation function of chaotic neural network （SLF model）, it presents a novel transient chaotic-neuron model by introducing the Legendre function and the Sigmoid activation function to compose the non-monotonous activation function. The reversed bifurcation and the maximum Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed. Based on the neuron model, a novel transient chaotic-neural network is proposed and applied to non-linear function-optimization and TSP problems. The simulation result indicates the validity of this novel transient chaotic-neural network.

Key words: chaotic neural network, Sigmoid function, Legendre function, Travelling Salesman Problem（TSP）, Lyapunov exponent

摘要： 针对混沌神经网络的单调激励函数，引入Legendre函数和Sigmoid函数组合作为非单调激励函数，构造了一种新的暂态混沌神经元模型（SLF模型），并给出了此混沌神经元的倒分岔图和最大Lyapunov指数时间演化图，利用该模型构建了一种暂态混沌神经网络，通过对非线性函数优化和TSP问题的求解验证了该模型的有效性。

关键词: 混沌神经网络, Sigmoid函数, Legendre函数, 旅行商问题（TSP）, Lyapunov指数