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DSWeb Dynamical Systems Software aims to collect all available software on dynamical systems theory. This project was originally launched during the special year Emerging Applications of Dynamical Systems, 1997/1998, at the Institute for Mathematics and its Applications. The information here includes functionality, platforms, languages, references, and contacts.

Please note that DSWeb is not responsible for any direct, indirect, special, incidental, or consequential damages arising from the use of the content provided here.

DynamicalSystems.jl (Julia)

Prize Winner - DSWeb 2018 Software Contest, Undergraduate/Graduate Student Category

By George Datseris
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DynamicalSystems.jl is a software library for the exploration of chaos and nonlinear dynamics. It is written entirely in Julia, a new programming language with large potential. From a technical viewpoint, DynamicalSystems.jl is composed of (currently) four packages for the Julia language and is not an independent application. DynamicalSystems.jl is available via Julia's package manager or via Download on GitHub, where you also find a complete documentation.

The ultimate goal for DynamicalSystems.jl is to be a useful library for students and scientists working on chaos, nonlinear dynamics and in general dynamical systems. The authors do not provide ‘‘just code’’, but also detailed descriptions and references for as many methods as possible. In addition, we strive for conciseness, transparency, performance, accuracy and reliability.

All information is contained within the .pdf file "GeorgeDatseris_DSWeb2018.pdf". There you fill find the description of the software DynamicalSystems.jl, along with everything else necessary for this application.

Some examples are contained in the "supplement.zip".

KeywordsJulia, chaos, nonlinear dynamics
Model
  • Maps
  • ODEs
Software Type
  • Package
  • Library
Language
  • Julia
Platform
  • Linux
  • Windows
  • MacOS
Availability
Contact Person
References to Papers

[1] Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B. Shah. Julia: A Fresh Approach to Numerical Computing. SIAM Review, 59(1):65–98, jan 2017.

[2] George Datseris. DynamicalSystems.jl documentation page. https://juliadynamics.github.io/DynamicalSystems.jl/latest/. Accessed: June 25, 2018.

[3] George Datseris. DynamicalSystems.jl: A julia software library for chaos and nonlinear dynamics. Journal of Open Source Software, 3(23):598, mar 2018.

[4] Karlheinz Geist, Ulrich Parlitz, and Werner Lauterborn. Comparison of Different Methods for Computing Lyapunov Exponents. Progress of Theoretical Physics, 83(5):875–893, 1990.

[5] M. Henon. A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50(1):69–77, feb 1976.

[6] Christopher Rackauckas. A comparison of DifferentialEquations.jl with ode solvers from different computer languages. http://www.stochasticlifestyle.com/ comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran/. Accessed: June 25, 2018.

[7] Christopher Rackauckas and Qing Nie. DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia. Journal of Open Research Software, 5, may 2017.

[8] Ch. Skokos, T.C. Bountis, and Ch. Antonopoulos. Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method. Physica D: Nonlinear Phenomena, 231(1):30–54, jul 2007. 9

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