A New Reliable Numerical Method for Computing Chaotic Solutions of Dynamical Systems: The Chen Attractor Case

Abstract : This paper describes a new reliable numerical method for computing chaotic solutions of dynamical systems and, in special cases, is applied to Chen strange attractor. The numerical precision of the computation is finely mastered.We introduce a modification of the method of power series for the construction of approximate solutions of the Chen system together with forward/backward control of the precision. As a test for the method, we obtained the region of convergence of series and researched the behavior of the trajectories on this attractor. The results of a numerical experiment are presented.
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René Lozi, Alexander Pchelintsev. A New Reliable Numerical Method for Computing Chaotic Solutions of Dynamical Systems: The Chen Attractor Case. International Journal of Bifurcation and Chaos, World Scientific Publishing, 2015, 25 (13), pp.1550187. ⟨http://www.worldscientific.com/doi/abs/10.1142/S0218127415501874⟩. ⟨10.1142/S0218127415501874⟩. ⟨hal-01323625⟩

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