Integrable Deformations of Three-Dimensional Chaotic Systems

Abstract

The integrable deformation method for a three-dimensional Hamilton–Poisson system consists in alteration of its constants of motion in order to obtain a new Hamilton–Poisson system. We assume that a three-dimensional system of differential equations has a Hamilton–Poisson part and a nonconservative part. We give integrable deformations of the Hamilton–Poisson part and, adding the nonconservative part, we obtain integrable deformations of the considered three-dimensional system of differential equations. In particular, applying this method to chaotic systems may lead to new systems with chaotic behavior. We use this method to obtain integrable deformations of Lorenz, Chen, and Rössler systems. Using particular deformation functions, we have pointed out some deformations of the above-mentioned attractors.