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Evolutionary Algorithm Based Solution of Rössler Chaotic System Using Bernstein Polynomials

Chaotic systems have gained enormous research attention since the pioneering work of Lorenz. Rössler system stands among the extensively studied classical chaotic models. This paper proposes a technique based on Bernstein Polynomial Basis Function to convert the three-dimensional
 Rössler system of Ordinary Differential Equations (ODEs) into an error minimization problem. First, the properties of Bernstein Polynomials are applied to derive the fitness function of Rössler chaotic system. Second, in order to obtain the values of unknown Bernstein coefficients
 to optimize the fitness function, the problem is solved using two versatile algorithms from the family of Evolutionary Algorithms (EAs), Genetic Algorithm (GA) hybridized with Interior Point Algorithm (IPA) and Differential Algorithm (DE). For validity of the proposed technique, simulation
 results are provided which verify the global stability of error dynamics and provide accurate estimation of the desired parameters.