Stability and Hopf bifurcation on four-neuron neural networks with inertia and multiple delays

In this paper, the four-neuron inertial neural system with multiple delays is proposed. By analyzing the associated transcendental characteristic equation, the linear stability of the model is investigated and Hopf bifurcation of the trivial equilibrium point is demonstrated. Periodic solutions bifurcating from the trivial equilibrium point are obtained analytically by using the Perturbation scheme without the normal form method and center manifold theory. Finally, numerical simulations well support the theoretical analysis.