Stability and hopf bifurcation of fractional complex–valued BAM neural networks with multiple time delays.

• The high-order fractional complex-valued BAM neural networks are proposed and their sufficient stability conditions are given. • Taking time delay as a bifurcation parameter, the general Hopf bifurcation conditions of fractional complex-valued BAM neural networks are obtained. • The relationship between fractional order and critical bifurcation point is also discussed. In this paper dynamical behaviors of a class of high–order fractional complex–valued bidirectional associative memory neural networks with multiple time delays are investigated. Firstly, they are reduced to real–valued systems by separating the real and imaginary parts. Then, stability criteria of fractional complex–valued bidirectional associative memory neural networks without delay are obtained. Concerning the delay case, the time delay is set as a bifurcation parameter and the condition of Hopf bifurcation is given by analyzing roots of characteristic equations. Finally, two numerical examples are presented and illustrate that Hopf bifurcation does happen when time delay exceeds the critical value. [ABSTRACT FROM AUTHOR]