A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities

René Lozi (1) , Vasily A. Pogonin (2) , Alexander N. Pchelintsev (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 T S T U - Tambov State Technical University

In this article the authors describe the method of construction of approximate chaotic solutions of dynamical model equations with quadratic nonlinearities in a general form using a new accurate numerical method. Numerous systems of chaotic dynamical systems of this type are studied in modern literature. The authors find the region of convergence of the method and offer an algorithm of construction and several criteria to check the accuracy of the approximate chaotic solutions.

Mots clés: almost periodic function; attractor; Lorenz system; Chen system; Nose-Hoover oscillator; power series; region of convergence

Domaines: Systèmes dynamiques [math.DS]

René Lozi, Vasily A. Pogonin, Alexander N. Pchelintsev. A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities. Chaos, Solitons & Fractals, 2016, 91, pp.108-114. ⟨10.1016/j.chaos.2016.05.010⟩. ⟨hal-01319597⟩