Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions

Multistability is an important dynamical property in neural networks in order to enable certain applications where monostable networks could be computationally restrictive. This paper studies some multistability properties for a class of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions. Based on local inhibition, conditions for globally exponential attractivity are established. These conditions allow coexistence of stable and unstable equilibrium points. By constructing some energy-like functions, complete convergence is studied.