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<p>In this article, we study the nonlinear dynamic Selkov system with fractional derivatives of the Gerasimov-Caputo type of variable orders and variable coefficients, which is a&#xa0;Cauchy problem. Some issues of the existence and uniqueness of a&#xa0;solution to this Cauchy problem are considered. The Adams-Bashforth-Multon numerical method from the family of predictor-corrector methods is chosen as an algorithm for studying this system. The numerical algorithm is used to visualize the results of the study: bifurcation diagrams, oscillograms, and phase trajectories are constructed depending on the characteristic time scale. Using bifurcation diagrams, various dynamic modes of the Selkov fractional oscillator are identified.</p>

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Study of dynamic modes of fractional Selkov oscillator with variable coefficients using bifurcation diagrams

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Roman I. Parovik

摘要

In this article, we study the nonlinear dynamic Selkov system with fractional derivatives of the Gerasimov-Caputo type of variable orders and variable coefficients, which is a Cauchy problem. Some issues of the existence and uniqueness of a solution to this Cauchy problem are considered. The Adams-Bashforth-Multon numerical method from the family of predictor-corrector methods is chosen as an algorithm for studying this system. The numerical algorithm is used to visualize the results of the study: bifurcation diagrams, oscillograms, and phase trajectories are constructed depending on the characteristic time scale. Using bifurcation diagrams, various dynamic modes of the Selkov fractional oscillator are identified.