Exponential attractivity of positive inertial neural networks in bidirectional associative memory model with heterogeneous delays

In this paper, the positivity of solutions and global exponential attractivity of a unique positive equilibrium point (EP) are studied for inertial neural networks described by a Hopfield-type bidirectional associative memory model with heterogeneous time-varying delays. We first exploit conditions on the damping coefficients and self excitation rates to establish state transformations, which can help to reduce the damping terms in the model. Based on novel comparison techniques developed from the theory of monotone dynamical systems, we then derive tractable conditions through M-matrix involving self excitation coefficients and connection weights to ensure the positivity of solutions and the existence of a unique EP corresponding to each input vector. The derived conditions are then utilized to show that the unique EP is positive and globally attractive. The efficacy of the obtained results is demonstrated by given numerical simulations.