Convergent and oscillatory activation dynamics for cascades of neural nets with nearest neighbor competitive or cooperative interactions

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It is shown that a cascade of the neural net n0 into the net n1 has oscillatory (convergent) dynamics if the nets n0 and n1 have oscillatory (convergent) dynamics and the net n1 has a special structure. The special structure required of n1 is that it consists of a finite number of units which can be arranged along a line segment with only nearest neighbor connections between units and where each adjacent pair of units interacts in either a mutally inhibitory manner or in a mutually excitatory manner. These nets, described in Hirsch (1989), have convergent dynamics if given constant input, by a result of Smillie (1984), and have oscillatory dynamics if given oscillatory input, by a result of the author (1990).

Original languageEnglish (US)
Pages (from-to)41-46
Number of pages6
JournalNeural Networks
Issue number1
StatePublished - 1991



  • Cascade
  • Convergent dynamics
  • Oscillatory dynamics
  • Tridiagonal competitive-cooperative systems

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence

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