Bifurcation Analysis of a Fractional-Order Bidirectional Associative Memory Neural Network with Multiple Delays

The bidirectional associative memory (BAM) neural network has the capability to store hetero-associative pattern pairs, which has high requirements for stability. This paper inquires into Hopf bifurcation of fractional-order bidirectional associative memory neural network (FOBAMNN) and implants three types of delays into the FOBAMNN. Namely leakage delay, self-connection delay, and communication delay, both of which are unequal. Drawing support from matrix eigenvalue theory, stability theory of fractional differential equations and bifurcation technology, The delay-dependent stability criterion and bifurcation point of the model are established by exploiting the characteristic polynomial. Afterwards, the self-connection delay or leakage delay is selected as the bifurcation parameter, and the unselected delay of the two is fixed in its stable interval, so as to obtain the condition of bifurcation. The results show that different types of delay affect the stability of the system. Simultaneously, once the delay outreaches the critical value of bifurcation, the stability of the model will be wrecked. Thereupon, in the application, we should adopt small delays to maintain the stability of the system. We illustrate that the leakage delay and self-connection delay can affect the stability of FOBAMNN. And the calculation method of the critical value of the delay will also be given. At length, the authenticity of the developed key fruits is  elucidated via numerical simulations.