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On a generalized Klausmeier model.

Martha Paola Cruz de la Cruz¹, Daniel Alfonso Santiesteban¹, Luis Miguel Martín Álvarez¹

¹Faculty of Mathematics, Autonomous University of Guerrero, Mexico.

Mathematical Biosciences and Engineering : MBE

|November 3, 2023

Summary

This study introduces a generalized Klausmeier model using local fractional derivatives, enhancing its applicability. The research analyzes model stability and solves an inverse problem with real-world data.

Keywords:

Klausmeier model fractional derivative homotopic perturbation method inverse problem stability analysis

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Area of Science:

Mathematical modeling
Fractional calculus
Nonlinear dynamics

Background:

The Klausmeier model describes pattern formation.
Integer derivatives limit model applicability.
Local fractional derivatives offer broader system analysis.

Purpose of the Study:

Generalize the Klausmeier model using local fractional derivatives.
Analyze the stability of the new model.
Apply the model to solve a real-world inverse problem.

Main Methods:

Local fractional derivative formulation.
Stability analysis techniques.
Homotopic perturbation method.
Inverse problem solution using real data.

Main Results:

A generalized Klausmeier model with enhanced flexibility.
Comprehensive stability analysis of the fractional model.
Successful application to a real data set, demonstrating practical utility.

Conclusions:

The generalized Klausmeier model with local fractional derivatives is a robust framework.
The model's stability is confirmed through rigorous analysis.
The study validates the model's effectiveness in solving inverse problems with real data.