Dynamics of chain-structure neural networks and its comparative analysis with different structures of ring and star
The chain structure widely exists in various complex systems,however,there are few studies on the bifur-cation dynamics of complex networks with chain structure.Taking neural network as an example,this paper studies the bifurcation dynamics of high-dimensional neural network models with chain structure and multiple delays.The recursion formulas of the characteristic polynomial varying with the number of neuron nodes is listed by the methods of the flow graph decomposition and global element substitution.Thereby,the distribution of the roots on the characteristic polyno-mial equation is analyzed.Afterwards,considering the effect of neurotransmitter transmission delay on the stability of the system,the critical value leading to the topological mutation of the system is obtained.Finally,the correctness of the theories are verified by numerical simulations,and the dynamics on neural networks of different structures including chain structure,star structure and ring structure are analyzed in comparison with simulated experiments for acquiring the influence of structural differences on bifurcation dynamics of neural networks.
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