Fractality in a delayed-prey-predator ecological system with Allee effects

TL;DR

This paper investigates a delayed prey-predator model with Allee effects, revealing complex dynamics including stability conditions, periodic solutions, and fractal trajectories, highlighting the system's cooperative nature.

Contribution

It introduces a novel delayed discrete-time prey-predator model with Allee effects and analyzes its stability, periodicity, and fractal properties computationally.

Findings

Stability conditions for equilibria are established.

Multiple periodic solutions are identified.

High fractality observed in population trajectories.

Abstract

A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of equilibria are investigated with several illustrating examples. In addition, several periodic solutions were achieved. Furthermore, high degree of fractality of the prey-predator population trajectories is observed when the system is sufficiently delayed. This system has turned out to be a cooperative system, which is depicted using fractal dimension.