Lie symmetry and optimal control of non-linear fractional-order chaotic financial system: Applying some evolutionary algorithms

The importance and necessity of studying the chaos phenomenon is due to the fact that the necessary and strong motivations for analyzing this non-linear phenomenon will clarify the grounds for the presence and occurrence of chaos and also its effects on the performance of systems. The purpose of this research is to investigate how to optimally control a nonlinear fractional-order chaotic financial system using evolutionary algorithms. Particle swarm optimization method and genetic algorithms were used to solve the problem of optimal control of financial system. In addition, Lie symmetries for the proposed model were calculated and the results were presented. The results of the control applied to the model can control the chaotic financial system. All the results obtained for the particle swarm optimization method show that this method has also been very successful and has results very close to the genetic algorithm method.

کلیدواژه ها:

Lie symmetry ، Optimal control ، Chaotic financial system ، evolutionary algorithms