Control of the Bifurcation Behaviors of Delayed Fractional-Order Neural Networks with Cooperation–Competition Topology

In the real world, the competition and cooperation relationship exists in numerous systems. For instance, the competition–cooperation structure of a biological neural network is determined by the excitatory and inhibitory effects of neurons. The dynamic behaviors of a neural network model with a competition–cooperation structure are studied in this article, focusing particularly on the bifurcation and control problems. By selecting time delay as the parameter, a new sufficient condition for Hopf bifurcation is given and the impact of the fractional order on bifurcation behavior is determined for the network. Furthermore, a time-delay feedback controller is introduced to manage Hopf bifurcation behaviors, and, meanwhile, the stability domain is expanded. Our findings indicate that both fractional order and time delay play a crucial role in controlling the stability and Hopf bifurcation of the given model. Lastly, the accuracy of our theoretical results is verified through several numerical simulations, and the impact of control parameters on the bifurcation behavior of the network model is discussed in detail.