Hopf bifurcation and chaos in an inertial neuron system with coupled delay

In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the network 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 manifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincaré 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.

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