A novel analysis of Hopf bifurcation for a fractional-order neural network involving mixed delays

Abstract This paper provides an extensive binary fractional-order neural network system with mixed delays consisting of two discrete delays and two distributed delays and emphasizes its bifurcating methods and theories. First, the original system is transformed into a five-neuron fractional-order neural network with four delays by introducing three virtual neurons. And then we select different delays as parameters inducing bifurcation to determine the ranges of guaranteeing the steady state response of the system. Some sufficient conditions for the occurrence of Hopf bifurcation are established. In the end, the correctness of the obtained conclusions is verified with the support of numerical simulations. It is found that both discrete and distributed delays play a key role in the Hopf bifurcation of fractional-order neural networks, especially the mean delay in distributed term has a great impact on the critical values controlling bifurcation.