View in EDS

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

Saved in:
Bibliographic Details
Title: A Study of the Efficiency of Parallel Computing for Constructing Bifurcation Diagrams of the Fractional Selkov Oscillator with Variable Coefficients and Memory.
Authors: Tverdyi, Dmitriy, Parovik, Roman
Source: Computation; Feb2026, Vol. 14 Issue 2, p32, 20p
Abstract: This paper presents a comprehensive performance analysis and practical implementation of a parallel algorithm for constructing bifurcation diagrams of the fractional Selkov oscillator with variable coefficients and memory (SFO). The primary contribution lies in the systematic benchmarking and validation of a coarse-grained parallelization strategy (MapReduce) applied to a computationally intensive class of problems—fractional-order systems with hereditary effects. We investigate the efficiency of a parallel algorithm that leverages central processing unit (CPU) capabilities to compute bifurcation diagrams of the Selkov fractional oscillator as a function of the characteristic time scale. The parallel algorithm is implemented in the ABMSelkovFracSim 2.0 software package using Python 3.13. This package also incorporates the Adams–Bashforth–Moulton numerical algorithm for obtaining numerical solutions to the Selkov fractional oscillator, thereby accounting for heredity (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 to ensure dimensional consistency in the model equations. This paper evaluates the efficiency, speedup, and cost of the parallel algorithm, and determines its optimal configuration based on the number of worker processes. The optimal number of processes required to achieve maximum efficiency for the algorithm is determined. We apply the TAECO approach to evaluate the efficiency of the parallel algorithm: T (execution time), A (acceleration), E (efficiency), C (cost), O (cost optimality index). Graphs illustrating the efficiency characteristics of the parallel algorithm as functions of the number of CPU processes are provided. [ABSTRACT FROM AUTHOR]
Copyright of Computation is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Complementary Index
Description
Abstract:This paper presents a comprehensive performance analysis and practical implementation of a parallel algorithm for constructing bifurcation diagrams of the fractional Selkov oscillator with variable coefficients and memory (SFO). The primary contribution lies in the systematic benchmarking and validation of a coarse-grained parallelization strategy (MapReduce) applied to a computationally intensive class of problems—fractional-order systems with hereditary effects. We investigate the efficiency of a parallel algorithm that leverages central processing unit (CPU) capabilities to compute bifurcation diagrams of the Selkov fractional oscillator as a function of the characteristic time scale. The parallel algorithm is implemented in the ABMSelkovFracSim 2.0 software package using Python 3.13. This package also incorporates the Adams–Bashforth–Moulton numerical algorithm for obtaining numerical solutions to the Selkov fractional oscillator, thereby accounting for heredity (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 to ensure dimensional consistency in the model equations. This paper evaluates the efficiency, speedup, and cost of the parallel algorithm, and determines its optimal configuration based on the number of worker processes. The optimal number of processes required to achieve maximum efficiency for the algorithm is determined. We apply the TAECO approach to evaluate the efficiency of the parallel algorithm: T (execution time), A (acceleration), E (efficiency), C (cost), O (cost optimality index). Graphs illustrating the efficiency characteristics of the parallel algorithm as functions of the number of CPU processes are provided. [ABSTRACT FROM AUTHOR]
ISSN:20793197
DOI:10.3390/computation14020032