Stability and Bifurcation Analysis of Delayed Neural Network Using Harmonic Balance Approach

Neural networks are commonly used to model brain functions and to resolve a variety of information that the brain receives. The earlier methods of centre manifold and multiple scales of order reduction of a delayed nonlinear system offer a serious challenge in analyzing Hopf bifurcation of a general delayed system. To overcome this challenge a standard procedure called Harmonic balance approach is used to analyze the stability and bifurcations of limit cycles. This paper analysed the bifurcation and stability for Hopfield network employing a two delays neural network. Using Harmonic balance approach, we have carried out Hopf bifurcation and stability analysis to obtain the periodic solutions. The stability of the bifurcated periodic solutions is examined along with the theoretical analysis. Nyquist criterion has been used to determine stability of the model. The critical values under which Hopf bifurcation occurs is determined. The analysis reveals that the stability of the solutions is guaranteed only inside the interval from 0.6 to 1.1. Results of mathematical simulation of frequency, phase and waveform with different phase angles are also presented.