Synthesis of Dynamical Systems with Chaotic Attractors

This paper discusses dynamical system synthesis with strange chaotic attractors. Such dynamical systems have abstract mathematical meaning but can be used to solve different applied problems. Two approaches for the formation of strange attractors are proposed. The first approach is a direct approach based on searching the coefficients of the nonlinear differential equation system that satisfy the required conditions for Lyapunov exponents and Kaplan–Yorke dimension. The second approach is an indirect approach based on methods and models of spacecraft attitude dynamics. The search for strange attractors is conducted using the differential evolution algorithm. Some new strange attractors are synthesized and analyzed. The analysis involves obtaining Lyapunov exponents, Kaplan–Yorke dimensions, and bifurcation diagrams.