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Heuristic computing with active set method for the nonlinear Rabinovich-Fabrikant model.

Zulqurnain Sabir1,2, Dumitru Baleanu3,4,5,6, Sharifah E Alhazmi7

  • 1Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.

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Summary

A new stochastic computing approach using artificial neural networks, genetic algorithm, and active set methods (ANNs-GAAS) reliably solves the nonlinear Rabinovich-Fabrikant model with high accuracy.

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Active set methodArtificial neural networksGenetic algorithmNumerical solutionsRabinovich-Fabrikant

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Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Artificial Intelligence

Background:

  • The Rabinovich-Fabrikant model is a complex nonlinear system involving three ordinary differential equations.
  • Solving such nonlinear models often requires robust and accurate numerical methods.

Purpose of the Study:

  • To introduce and validate a novel heuristic approach for solving the nonlinear Rabinovich-Fabrikant model.
  • To demonstrate the reliability and accuracy of the proposed computational method.

Main Methods:

  • The study employs a hybrid computational technique, termed ANNs-GAAS, combining artificial neural networks (ANNs) with a global heuristic genetic algorithm (GA) and local search active set (AS) methodologies.
  • A merit function is constructed based on the differential Rabinovich-Fabrikant model.
  • The ANNs-GAAS approach utilizes a neural network structure with ten neurons and a log-sigmoid transfer function.

Main Results:

  • The ANNs-GAAS method provides simple, reliable, and accurate solutions for the Rabinovich-Fabrikant model.
  • The optimization of the merit function using the GAAS method yields high-precision results.
  • The absolute errors achieved are in the range of 10-07 to 10-08.
  • Comparisons with conventional solutions confirm the method's correctness.

Conclusions:

  • The proposed ANNs-GAAS approach is a validated and effective technique for solving the nonlinear Rabinovich-Fabrikant model.
  • The method's reliability is further substantiated through various statistical analyses.
  • This work contributes a robust computational tool for nonlinear dynamics research.