Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models

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We present a set of four three-dimensional models inspired by predator–prey systems involving a basal food source, prey, and predator, with each model including a variation in the predator’s behaviour. We investigate these models across a wide range of parameter space and present results for various behaviours, including chaotic and hyper-chaotic behaviour. We find that increased consumption of the basal food source benefits species’ survival for some of our models whilst being detrimental to others. In all of the models, increased consumption reduces the extent to which over-predation leads to the extinction of the prey. Mutation is found to have a more significant impact on stability if the mutant is an omnivore, with no chaotic behaviour occurring in certain regions of parameter space. Connections have been made between each model’s largest Lyapunov Exponent and the Hurst exponent with the Hurst exponent proving to be a reliable indicator of chaos. Machine learning methods have been used to predict the largest Lyapunov exponent using the corresponding Hurst exponent with errors presented for each method.
Original languageEnglish
Article number129146
Pages (from-to)1-25
Number of pages25
JournalPhysica A: Statistical Mechanics and its Applications
Early online date19 Aug 2023
Publication statusPublished (in print/issue) - 15 Oct 2023

Bibliographical note

Funding Information:
A. McAllister is funded by the Department for the Economy .

Publisher Copyright:
© 2023 The Author(s)


  • Three dimensional model
  • Coupled logistic maps
  • Hurst exponent
  • Lyapunov exponents
  • Chaotic dynamics
  • Machine learning


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