Abstract
Using the calculation of local Lyapunov exponents the influence of the stationary noise on statistical characteristics of intermittent generalized synchronization and critical coupling parameter value corresponding to the generalized synchronization regime onset has been studied. Two unidirectionally and mutually coupled chaotic Lorenz oscillators with a complex (two-sheeted) topology of attractors, characterized by the jump-intermittency, have been chosen as the systems under study. The dependence of the critical value of the coupling parameter on the noise intensity has been estimated. We calculated such general characteristics of the intermittency as the distributions of the laminar phase lengths for fixed values of the coupling parameter and the dependence of the mean length of the laminar phases on the criticality parameter. We have shown that the numerically obtained statistical characteristics greatly correspond to theoretical exponential laws. Obtained results are in a good agreement with the results of other works and demonstrate that the method of local Lyapunov exponents has significant stability to noise and has a strong potential to be applied for different nonlinear systems coupled unidirectionally or mutually.
Supported by the grant from the President of Russian Federation according to the research project No. MD-21.2020.2.
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Notes
- 1.
For relatively small values of the noise intensity comparable with the amplitude of own oscillations of the system the boundary value of the GS regime onset does not change dramatically, and in the case of unidirectional coupling even remains almost constant.
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Evstifeev, E.V., Moskalenko, O.I. (2021). Noise Influence on the Estimation of Characteristics of Intermittent Generalized Synchronization Using Local Lyapunov Exponents. In: Balandin, D., Barkalov, K., Gergel, V., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2020. Communications in Computer and Information Science, vol 1413. Springer, Cham. https://doi.org/10.1007/978-3-030-78759-2_14
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