Solution of the Boolean Markus-Yamabe problem

The main point in the design of content addressable memory would be under w hat conditions the state possessing the total information can attract all o ther states in the phase of the system. The problem can be formulated as a global asymptotic stability problem of Boolean dynamical systems. In this a rticle we give a complete answer to this global asymptotic stability proble m. The conditions employed involve the Hamming distance on the phase space {0, 1}(n) as well as the spectral condition on the Jacobian Boolean matrix of F: {0, 1}(n) --> {0, 1}(n) evaluated at each point of {0, 1}(n). This ar ticle furnishes a complete solution of the Boolean Markus-Yamabe problem. ( C) 1999 Academic Press.