Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the...

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Bibliographic Details
Published inApplied sciences Vol. 11; no. 15; p. 6955
Main Authors Rysak, Andrzej, Gregorczyk, Magdalena
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2021
Subjects
Algorithms
chaos
differential transform method
Dynamic characteristics
Dynamical systems
fractional differential equations
Integration
Methods
nonlinear systems
Quality assessment
System effectiveness
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Summary:This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.
ISSN:2076-3417
2076-3417
DOI:10.3390/app11156955