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

Abstract

10 pages; 3 figures.International audienceThis paper describes a new reliable numerical method for computing chaotic solutions of dynamicalsystems and, in special cases, is applied to Chen strange attractor. The numerical precision ofthe computation is finely mastered.We introduce a modification of the method of power series forthe construction of approximate solutions of the Chen system together with forward/backwardcontrol of the precision. As a test for the method, we obtained the region of convergence ofseries and researched the behavior of the trajectories on this attractor. The results of a numericalexperiment are presented

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

“…Also, an estimate of the region of convergence of the power series is obtained, and some criteria for checking the accuracy of the approximate chaotic solutions is given in this article. Recently such an approach has been applied to the Lorenz and Chen systems [22,23]. Here, we generalize our results for the systems in the form (1).…”

“…If a value of the accuracy ε p is too big large, then the point of the trajectory will go to infinity when we compute backward due to strong unstability. In [22] ε p = 10 −50 for the Lorenz system, in [23] ε p = 10 −80 and 10 −53 for the Chen system. 4.…”

An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems

“…T ε p The Lorenz system [1,37] 6.827 10 −50 The Chen system [16,17,38] 8. The chaotic behaviour of the trajectories is observed N = 5, H = 3 and I = 0.4 (see Fig.…”

“…Also we use the configuration analysis of the approximate chaotic solution to check the accuracy it. In this case, we calculate the maximum degrees of piecewise polynomials which must be the same at the forward and backward time as in the articles [38,39].…”

The Effects of Padé Numerical Integration in Simulation of Conservative Chaotic Systems

“…The influence of numerical methods on discrete models of chaotic systems is widely studied. While highly accurate numerical methods for chaotic problems integration have been recently developed [1,2], some studies reveal the negative aspects of popular discretization techniques [3,4] and discover the additional properties introduced by numerical errors [5]. Thus, when new class of integration methods appears, the collateral numerical effects are of certain interest.…”