A conceptual predator-prey model with super-long transients

TL;DR

This paper introduces a simple predator-prey model inspired by the logistic map that captures complex ecological dynamics, including super-long transients, regime shifts, and multiple time scales, serving as a conceptual tool for ecosystem analysis.

Contribution

It presents a novel, minimalistic predator-prey model that reproduces complex ecological behaviors and super-long transients, enhancing understanding of ecosystem resilience and dynamics.

Findings

Model exhibits coexistence of multiple time scales.

Captures super-long transients and regime shifts.

Replicates chaotic and cyclical population behaviors.

Abstract

Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute to the coexistence of multiple time scales, adding to the complexity of the system. Typical dynamics in ecosystems, such as the persistence and coexistence of population cycles and chaotic behaviors, the emergence of super-long transients, regime shifts, and the quantifying of resilience, are encapsulated within this single model. The simplicity of our model allows for detailed analysis, reinforcing its potential as a conceptual tool for understanding ecosystems deeply.