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<p>The paper investigates a chain of two coupled linear Berlage oscillators, which describes the interaction of two dislocation sources of geoacoustic emission. The questions of the existence and uniqueness of the solution were investigated, and a theorem based on the principle of compressive maps from functional analysis was proved. The stability of the null solution of the model is investigated, as well as the stability over long times is investigated, all the results were formulated in the form of theorems. The paper also presents the elements of numerical analysis based on four numerical methods (the Rosenbrock method of the 4th order of accuracy, Radau, BDF, and LSODA). The Rosenbrock method is implemented in Python, while the rest of the methods are taken from the Scipy library. Numerical analysis was used to obtain the results of the study, which are visualized in the form of graphs of waveforms, spectra, phase trajectories, as well as graphs of the dependence of the order of accuracy on the step of calculations under various conditions: the presence of rigidity, instability, etc.</p>

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INVESTIGATION OF A SYSTEM OF TWO COUPLED LINEAR OSCILLATORS WITH NON-CONSTANT COEFFICIENTS

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Darya F. Sergienko,
  • Roman R. Parovik

摘要

The paper investigates a chain of two coupled linear Berlage oscillators, which describes the interaction of two dislocation sources of geoacoustic emission. The questions of the existence and uniqueness of the solution were investigated, and a theorem based on the principle of compressive maps from functional analysis was proved. The stability of the null solution of the model is investigated, as well as the stability over long times is investigated, all the results were formulated in the form of theorems. The paper also presents the elements of numerical analysis based on four numerical methods (the Rosenbrock method of the 4th order of accuracy, Radau, BDF, and LSODA). The Rosenbrock method is implemented in Python, while the rest of the methods are taken from the Scipy library. Numerical analysis was used to obtain the results of the study, which are visualized in the form of graphs of waveforms, spectra, phase trajectories, as well as graphs of the dependence of the order of accuracy on the step of calculations under various conditions: the presence of rigidity, instability, etc.