Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube

作者：Di Marco Mauro; Forti Mauro^*; Grazzini Massimo; Pancioni Luca

来源：Neural Networks, 2014, 54: 38-48.

DOI：10.1016/j.neunet.2014.02.010

• Neural networks
• Multistability
• Differential variational inequalities
• Cooperative dynamical systems
• Nonsmooth dynamical systems

The paper considers nonsmooth neural networks described by a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs include the relevant class of neural networks, introduced by Li, Michel and Porod, described by linear systems evolving in a closed hypercube of R-n. The main result in the taper is a necessary and sufficient condition for multistability of DVIs with nonsymmetric and cooperative (nonnegative) interconnections between neurons. The condition is easily checkable and provides a sharp bound between DVIs that can store multiple patterns, as asymptotically stable equilibria, and those for which this is not possible. Numerical examples and simulations are presented to confirm and illustrate the theoretic findings.

• 出版日期2014-6