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On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems.

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Mathematical modeling and analysis of two-variable system with noninteger-order derivative.

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Updated: Jan 30, 2026

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Computational study of noninteger order system of predation.

Kolade M Owolabi1

  • 1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa and Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria.

Chaos (Woodbury, N.Y.)
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PubMed
Summary
This summary is machine-generated.

This study analyzes predator-prey dynamics using fractional differential equations. The research confirms stability analysis results through computer simulations, advancing ecological modeling.

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Area of Science:

  • Mathematical Biology
  • Dynamical Systems
  • Fractional Calculus

Background:

  • Predator-prey models are fundamental in ecology.
  • Fractional calculus offers a more nuanced approach to modeling time-dependent phenomena.
  • Understanding stability and bifurcations is crucial for ecological predictions.

Purpose of the Study:

  • To analyze the stability of equilibrium and Hopf bifurcation points in a three-component predator-prey model.
  • To investigate the application of Caputo and Atangana-Baleanu fractional derivatives in ecological modeling.
  • To validate numerical findings with simulation results.

Main Methods:

  • Discretization of time-fractional derivatives using a fractional Adams-Bashforth formula.
  • Linear stability analysis of the fractional predator-prey model.
  • Computer simulations to confirm analytical results.

Main Results:

  • The stability of the equilibrium point was analyzed.
  • Hopf bifurcation points were identified and analyzed.
  • Numerical simulations corroborated the theoretical stability analysis.

Conclusions:

  • Fractional derivatives provide a valuable framework for predator-prey dynamics.
  • The study successfully applied fractional calculus to ecological modeling.
  • The findings enhance the understanding of complex species interactions.