A Study of the Efficiency of Parallel Computing for Constructing Bifurcation Diagrams of the Fractional Selkov Oscillator with Variable Coefficients and Memory

This paper examines the efficiency of a parallel version of an algorithm that utilizes the capabilities of the central processing unit (CPU) to calculate bifurcation diagrams of the Selkov fractional oscillator depending on the characteristic time scale. The parallel version of the algorithm is implemented in the ABMSelkovFracSim 2.0 software package written in Python, which also includes the Adams-Bashforth-Multon numerical algorithm, which enables one to find a numerical solution to the Selkov fractional oscillator that takes into account heredity or memory effects. The Selkov fractional oscillator is a system of nonlinear ordinary differential equations with Gerasimov-Caputo derivatives of fractional order variables and non-constant coefficients, which include a characteristic time scale parameter for matching the dimensions in the model equations. The paper evaluates the efficiency, speedup, and cost of the parallel algorithm, and presents a calculation of its optimal cost depending on the number of CPU threads. The optimal number of threads required to achieve maximum efficiency of the algorithm is determined. The TAECO approach was chosen to evaluate the efficiency of the parallel algorithm: T (execution time), A (acceleration), E (efficiency), C (cost), O (cost optimality index). Graphs of the efficiency characteristics of the parallel algorithm depending on the number of CPU threads are provided.