Stability of cycles and survival in a jungle game with four species

The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The stability of all heteroclinic cycles in the network for the Jungl...

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Bibliographic Details
Published in:Dynamical systems (London, England) England), 2024-07, Vol.39 (3), p.389-407
Main Authors: Castro, Sofia B. S. D., Ferreira, Ana M. J., Labouriau, Isabel S.
Format: Article
Language:English
Subjects:
asymptotic stability
Cutting tools
essential asymptotic stability
Food chains
Games
Heteroclinic cycle
heteroclinic network
population dynamics
Stability
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Summary:The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The stability of all heteroclinic cycles in the network for the Jungle Game with four species determines that only three species coexist in the long-run, interacting under cyclic dominance as a Rock-Paper-Scissors Game. This is in stark contrast with other interactions involving four species, such as cyclic interaction and intraguild predation. We use the Jungle Game with four species to determine the success of a fourth species invading a population of Rock-Paper-Scissors players.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2024.2307515