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

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.