IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 1994 · 204 citations · 17 references
Natural SciencesMathematicsDynamical SystemsNeural CircuitryOptimizationNetwork StabilityNeural Circuit ModelingNeural CircuitsNeural NetworksStabilityStability TheoryAbsolute StabilityAbsolute Stability CriterionCircuit StabilityHopfield Networks
The main result in this paper is that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for Absolute Stability. The most significant theoretical implication is that the class of neural circuits with a negative semidefinite T is the largest class of circuits that can be employed for embedding and solving optimization problems without the risk of spurious responses.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Convergent activation dynamics in continuous time networks
Morris W. Hirsch · Neural Networks · 1989 · 599 citations · Full text