变频正弦混沌神经网络及其应用  

Frequency conversion sinusoidal chaotic neural network and its application

作　　者：胡志强[1,2] 李文静[1,2] 乔俊飞[1,2] 

机构地区：[1]北京工业大学信息学部,北京100124 [2]计算智能与智能系统北京市重点实验室,北京100124

出　　处：《物理学报》2017年第9期12-22,共11页Acta Physica Sinica

基　　金：国家自然科学基金重点项目(批准号:61533002);国家自然科学基金青年科学基金(批准号:61603009);国家杰出青年科学基金(批准号:61225016);中国博士后科学基金(批准号:2015M570910);朝阳区博士后研究基金(批准号:2015ZZ-6);北京工业大学基础研究基金(批准号:002000514315501)资助的课题~~

摘　　要：针对暂态混沌神经网络全局寻优能力受限的问题,提出了一种基于脑电波生物机制的新型混沌神经网络模型——变频正弦混沌神经网络.该模型将变频正弦函数和Sigmoid函数组合作为非单调激励函数,本文给出了该混沌神经元的倒分岔图及Lyapunov指数的时间演化图,分析了其动力学特性.进一步将该模型应用到非线性函数优化和组合优化问题上,并分析了参数的变化规律.仿真实验证明变频正弦混沌神经网络比暂态混沌神经网络及其他相关模型具有更好的全局寻优能力.The optimization performance of transiently chaotic neural network （TCNN） is affected by various factors such as chaotic characteristic, model parameters, and annealing function, and its capacity of global optimization is limited. It is demonstrated that the non-monotonic activation function can generate richer chaotic characteristic than the monotonic activation function in the TCNN model. Besides, the activation function involving neurobiological mechanism can not only reflect the rich brain activity in brain waves, but also enhance the non-linear dynamic characteristic, which may further improve the global optimization ability. Hence, a novel chaotic neuron model is proposed with the non-monotonic activation function based on the neurobiological mechanisms from the electroencephalogram. The electroencephalogram consists of five brain waves （i.e., a, t5, a, if, and 8 waves） which are defned by the quality and intensity of brain waves with different frequency bands ranging from 0.5 Hz to 100 Hz. The brain wave with a higher frequency and a lower amplitude represents a more active brain. Researches demonstrate that the five brain waves can be simplified into sinusoidal waves with different frequencies. Hence, a frequency conversion sinusoidal （FCS） function which has the consistent frequency range and features with brain waves is designed based on the above neurobiologieal mechanisms. Then a novel chaotic neuron model with non-monotonic activation function which is composed of the FCS function and sigmoid function, is proposed for richer chaotic dynamic characteristic. The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed, indicating that the proposed FCS neuron model owns richer chaotic dynamic characteristic than transiently chaotic neuron model due to its special non-monotonic activation function. Based on the neuron model, a novel transiently-chaotic neural network--frequency conversion sinusoidal chaotic neural network （FCSCNN）

关 键 词：混沌神经网络 脑电图 变频正弦混沌神经网络 组合优化 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]