In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained ...In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.展开更多
An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced w...An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays.When two delays are close to double Hopf bifurcation point,all solutions derived from the bifurcation are classified qualitatively and expressed explicitly.Numerical simulations are a good agreement with our theoretical analysis,and also already work in references.The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations.The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11202068 and 11032009)
文摘In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.
基金supported by the National Natural Science Foundation of China(Grant Nos.11872175,11572224,61603125 and 21130010)Young Talents Fund of Henan University of Economics and Law+1 种基金National Key Project Cultivation Project of Henan University of Economics and LawKey Research Project of Higher Education Institutions of Henan Province(Grant No.18A110003)。
文摘An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays.When two delays are close to double Hopf bifurcation point,all solutions derived from the bifurcation are classified qualitatively and expressed explicitly.Numerical simulations are a good agreement with our theoretical analysis,and also already work in references.The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations.The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.
