This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf ...This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results.展开更多
Up till the present moment,researchers have always featured the single-ring neural network.These investigations,however,disregard the link between rings in neural networks.This paper highlights a high-dimensional doub...Up till the present moment,researchers have always featured the single-ring neural network.These investigations,however,disregard the link between rings in neural networks.This paper highlights a high-dimensional double-ring neural network model with multiple time delays.The neural network has two rings of a shared node,where one ring has n neurons and the other has m+1 neurons.By utilizing the sum of time delays as the bifurcation parameter,the method of Coates’flow graph is applied to obtain the relevant characteristic equation.The stability of the neural network model with bicyclic structure is discussed by dissecting the characteristic equation,and the critical value of Hopf bifurcation is derived.The effect of the sum of time delays and the number of neurons on the stability of the model is extrapolated.The validity of the theory can be verified by numerical simulations.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11372102)
文摘This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results.
基金supported by the National Natural Science Foundation of China under Grant Nos.61573194,62073172,61877033the Natural Science Foundation of Jiangsu Province of China under Grant No.BK20181389。
文摘Up till the present moment,researchers have always featured the single-ring neural network.These investigations,however,disregard the link between rings in neural networks.This paper highlights a high-dimensional double-ring neural network model with multiple time delays.The neural network has two rings of a shared node,where one ring has n neurons and the other has m+1 neurons.By utilizing the sum of time delays as the bifurcation parameter,the method of Coates’flow graph is applied to obtain the relevant characteristic equation.The stability of the neural network model with bicyclic structure is discussed by dissecting the characteristic equation,and the critical value of Hopf bifurcation is derived.The effect of the sum of time delays and the number of neurons on the stability of the model is extrapolated.The validity of the theory can be verified by numerical simulations.
