Method of bifurcation analysis of cellular neural network for CPG models
Yijun Zhang, Zhu Qing-bao, Engang Tian · Control theory & applications · 2006
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 Poincare-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.