A proof of Kaszkurewicz and Bhaya´s conjecture on absolute stability of neural networks in two-neuron case

This letter presents a proof of Kaszkurewicz and Bhaya´s conjecture (1995) on the absolute stability of neural networks in the two-neuron case. The conjecture states that the necessary and sufficient condition for absolute stability of neural networks with an n×n interconnection matrix T is T∈I₀, where I₀ denotes the class of matrices T such that matrix (T-D₁)D₂ has all eigenvalues with negative real parts for arbitrary positive diagonal matrices D₁ and D₂ . A characterization condition for the I₀ class of matrices in the two-dimensional (2-D) case n=2 is also obtained