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

Christian Bick; Mikhail I. Rabinovich

doi:10.1080/14689360903322227

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 Journal › Article › Academic › peer-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 language	English
Pages (from-to)	97-110
Number of pages	14
Journal	Dynamical Systems
Volume	25
Issue number	1
DOIs	https://doi.org/10.1080/14689360903322227
Publication status	Published - 1 Mar 2010
Externally published	Yes

Keywords

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

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10.1080/14689360903322227

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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.",

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AU - Rabinovich, Mikhail I.

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N2 - 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.

AB - 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.

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KW - Neural computation

KW - Random networks

KW - Spatio-temporal coding

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

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Keywords

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