Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS
Volume 20, Issue 11, Pages 1842-1851Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2009.2032269
Keywords
Attractor networks; degenerate equilibrium; global attractivity; linear threshold activation function; multistability
Categories
Funding
- National Science Foundation of China [10825104]
- Specialized Research Fund for Doctoral Program [200806100002]
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Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model. On the basis of previous results on nondegenerate and degenerate equilibria in mathematics, we further elucidate all possible nontrivial global attractors. Our theoretical result provides precise descriptions on how the changes of network parameters affect the attractors' distribution and landscape, and it may give a feasible solution towards specifying attractors by specifying weights. Simulations are presented to illustrate the theoretical results.
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