Hopf Bifurcation and Chaos of A Class of Inertial Two-Neuron System with Time Delay

Abstract

A complete analysis of Hopf bifurcation and chaos for a class of inertial two-neuron system with time-delay is given in this paper. On the premise of analyzing the bifurcation condition of the system. PIS is used to induce Hop bifurcation and approximate periodic solution. A large number of simulations show that the error between the approximate periodic solution and the original periodic solution is very small, which directly reflects the properties of the periodic solution. Therefore, the use of the specification theorem and the central manifold theorem is avoided to carry out complex calculation. Finally, the chaotic behavior of the system is well demonstrated by simulation. So far, we have discussed the properties of a class of two neurons in detail. It lays a foundation for further discussion of more complex neural network systems.