On the occurrence of stable heteroclinic channels in Lotka-Volterra models

Christian Bick*, Mikhail I. Rabinovich

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The Lotka-Volterra (LV) equations can be used to model the behaviour of complex systems in nature. Trajectories in a stable heteroclinic channel (SHC) describe transient dynamics according to the winnerless competition principle in such a system. The existence of an SHC is guaranteed if the parameters of the LV equations satisfy a number of conditions. We study under what conditions a heteroclinic channel arises in a system where the coupling strengths are chosen randomly. These results describe the overall structure of the system dependent on the length of the channel. This relationship gives an estimation for the possible length of sequences of states in systems occurring in nature.

Original languageEnglish
Pages (from-to)97-110
Number of pages14
JournalDynamical Systems
Volume25
Issue number1
DOIs
Publication statusPublished - 1 Mar 2010
Externally publishedYes

Keywords

  • Dynamical systems
  • Lotka-Volterra model
  • Neural computation
  • Random networks
  • Spatio-temporal coding
  • Transient dynamics

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