Exploration of bifurcation dynamics for a type of neural system with three delays

Many problems of physical interest involve the nonlinear interaction of two oscillators with different frequencies. Such mode interactions are double Hopf bifurcation. In this paper, stability and double Hopf bifurcation dynamics are focused on for a multi-delay neural network when the combined influences of coupling delay and self-connection strength are taken into account. The complex dynamics near the critical point of weak resonance are derived using the perturbation scheme, which is different from the previously published works. Finally, numerical examples agree well with the main analysis. Double Hopf bifurcation dynamics play an important role in improving network systems and expanding their related application fields.