Multistability and enlarged basins of attraction in bidirectional associative memory neural networks

The multistability problem is discussed for 2n-dimensional bidirectional associative memory (BAM) neural networks with a general class of activation functions. By using analysis approach and decomposition of state space, ¿²ⁿ can be divided into 3ⁿ regions. 2ⁿ regions of them are positive invariant, and under some conditions, every invariant set has a locally exponentially stable equilibrium. Moreover, new attractive basin is investigated. It is larger than the positive invariant set. Finally, numerical simulations are carried out to illustrate the results.