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

Kolade M Owolabi1, Zakia Hammouch2

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

This study applies the Atangana-Baleanu derivative to model symbiosis systems, offering a novel approach for ecological dynamics. The new method captures complex behaviors in predator-prey and commensalism interactions.

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Area of Science:

  • Mathematical Biology
  • Dynamical Systems Theory
  • Fractional Calculus

Background:

  • Ecological systems, including predator-prey and commensalism, exhibit complex dynamics.
  • Traditional modeling approaches may not fully capture the nonlocal and nonsingular properties inherent in biological interactions.
  • The Atangana-Baleanu derivative offers unique mathematical properties suitable for advanced modeling.

Purpose of the Study:

  • To apply the Atangana-Baleanu derivative operator to model symbiosis systems.
  • To investigate the application of this derivative in describing commensalism and predator-prey processes.
  • To analyze the mathematical properties and potential of the Atangana-Baleanu derivative in ecological modeling.

Main Methods:

  • Application of the Atangana-Baleanu derivative operator to established ecological models.
  • Mathematical analysis of the resulting fractional dynamical systems.
  • Investigation of model behavior, including chaotic and spatiotemporal dynamics, for various fractional orders (α).

Main Results:

  • Successful application of the Atangana-Baleanu derivative to model ecological symbiosis.
  • Demonstration of the derivative's ability to capture nonlocal and nonsingular characteristics in biological systems.
  • Observation of chaotic and spatiotemporal patterns, particularly with fractional power α, indicating rich system behavior.

Conclusions:

  • The Atangana-Baleanu derivative provides a powerful and versatile tool for modeling complex ecological interactions.
  • Its unique properties, including Markovian and non-Markovian aspects, enhance the realism of symbiosis and predator-prey models.
  • Further research into fractional ecological models using this derivative can yield deeper insights into ecosystem dynamics.