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

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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