Modeling of fractional order chaotic systems using artificial bee colony optimization and ant colony optimization

摘要

In this paper, a modified Artificial Bee Colony algorithm is proposed. Then estimation of the parameters of fractional order chaotic systems is performed using the proposed Artificial Bee Colony algorithm and Ant Colony algorithm. For the purpose of modeling, four fractional order chaotic systems viz. Financial System, Chen System, Lorenz's system and 3 Cell Net system have been considered. Each chaotic system is defined by a set of fractional-order differential equations. These equations comprise of several variables - model parameters, derivative orders, and initial conditions. For the system's entire state and future values to be known, the values of all the parameters have to be estimated to a reasonable degree of accuracy. It is a general practice to use modern evolutionary algorithms to solve such problems. Simulations on both nature inspired optimization algorithms are performed and estimated values of parameters determined. Comparisons with existing scheme of Artificial Bee Colony based parameter estimation are also performed. Observations reveal that the results of the modified ABC algorithm outperform those of other techniques for all the four cases.