Approximating Numerical Solution of Lü Chaotic System using Bernstein Polynomials

Lu system is considered as one of the important models of three-dimensional chaotic systems. This paper presents numerical approximation of Lu chaotic system using Swarm Intelligence hybridized with Bernstein Polynomials. First, a three-dimensional Lu system represented by a set of first-order differential equations is converted in to an error minimization problem by applying the properties of Bernstein Polynomials. Then the values of unknown Bernstein coefficients which minimize the error function are obtained using Artificial Bee Colony which is a simple population-based global optimization algorithm from the family of Swarm Intelligence. For validity of the proposed scheme, simulations results are provided which demonstrated the effectiveness of the proposed method in accurately estimating the parameters of Lu chaotic system.