On a highly accurate numerical method for studying of the hidden attractors in the piecewise smooth Chua system
https://doi.org/10.25587/2411-9326-2025-3-113-134
Abstract
We consider an adaptation to the piecewise smooth Chua system of the previously developed high-precision numerical method for constructing approximations to unstable solutions of dynamic systems with quadratic nonlinearities on their attractors. Also, a modification of the Benettin–Wolf algorithm for calculating the characteristic Lyapunov exponents of the considered piecewise smooth system is obtained for the mode under consideration. A method based on the least squares method is developed, which makes possible to calculate the averaged estimate of the highest Lyapunov exponent based on the data on the behavior of the linearized dynamic system using a high-precision method over large time intervals. The following results are obtained for hidden attractors in the Chua system: 1) the fractal dimension of the hidden chaotic attractor based on the Poincar´e return statistics, 2) the values of the characteristic Lyapunov exponents for a stable cycle and a chaotic attractor with the use of the developed modification of the Benettin–Wolf algorithm; its efficiency is increased due to parallel computing.
About the Author
A. N. Pchelintsev
Tambov State Technical University
Russian Federation
Russian Federation
Alexander N. Pchelintsev
106 Sovetskaya Street, Tambov 392000
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For citations:
Pchelintsev A.N. On a highly accurate numerical method for studying of the hidden attractors in the piecewise smooth Chua system. Mathematical notes of NEFU. 2025;32(3):113-134. (In Russ.) https://doi.org/10.25587/2411-9326-2025-3-113-134
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