实现CPG模型的细胞神经网络的分支分析方法

Method of bifurcation analysis of cellular neural network for CPG models

中文关键词  细胞神经网络  周期解  中枢模式发生器  步态控制

英文关键词  cellular neural networks  periodic solution  central pattern generator  locomotion control

中文摘要

      传统细胞神经网络(CNN)的输出函数是不光滑的,难于研究其状态方程的分支情况.本文提出了用双曲函数近似分段线性输出函数,构成类似CNN系统.首先利用Poincaré-Bendixson定理和数值计算方法证明了新细胞状态方程存在稳定的周期解,然后通过局部分支理论计算出了使状态方程产生分支时偏置量的临界值,最后得出了偏置量的改变会影响状态方程振荡周期的结论,并通过仿真实验表明,在新CNN中得到的结论可以应用到CNN原型系统中,从而为通过CNN产生不同的CPG模式提供了理论依据.

英文摘要

      To analyze the bifurcation phenomena in cellular neural networks(CNN) state-equations,an analogy CNN is built in this paper with a sigmoid output-function instead of the traditional one.Firstly,through Poincaré-Bendixson theory and numerical calculation,it is proved that there exist periodic solutions of the new CNN.Secondly,an approach based on local bifurcation theory is introduced to find the critical parameter when periodic solutions vanish.Finally,a conclusion is drawn that a suitable periodic solution can be achieved by changing the value of the bias,and simulation experiments show that it is also valid in conventional CNN,which is an academic foundation to generate different patterns in central pattern generation(CPG) control strategy.