Exponential Transients in Continuous-Time Liapunov Systems

0404691 - UIVT-O 20030011 RIV NL eng J - Journal Article
Šíma, Jiří - Orponen, P.
Exponential Transients in Continuous-Time Liapunov Systems.
Theoretical Computer Science. Roč. 306, - (2003), s. 353-372. ISSN 0304-3975. E-ISSN 1879-2294
R&D Projects: GA AV ČR IAB2030007; GA ČR GA201/00/1489; GA ČR GA201/01/1192
Institutional research plan: AV0Z1030915
Keywords : dynamical systems * continuous time * Hopfield network * Liapunov function * convergence time
Subject RIV: BA - General Mathematics
Impact factor: 0.764, year: 2003

We consider the convergence behavior of a class of continuous-time dynamical systems corresponding to so called symmetric Hopfield nets studied in neural networks theory. We prove that such systems may have transient times that are exponential in the system dimension (i.e. number of "neurons"), despite the fact that their dynamics are controlled by Liapunov functions. This result stands in contrast to many proposed uses of such systems in e.g. combinatorial optimization applications, in which it is often...
Permanent Link: http://hdl.handle.net/11104/0124930