Chaos in Chen's system with a fractional order
From MaRDI portal
Publication:1766645
DOI10.1016/j.chaos.2004.02.013zbMath1060.37026OpenAlexW2027955822MaRDI QIDQ1766645
Publication date: 8 March 2005
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.chaos.2004.02.013
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Determining Lyapunov exponents from a time series
- An algorithm for the numerical solution of differential equations of fractional order
- A predictor-corrector approach for the numerical solution of fractional differential equations
- A practical method for calculating largest Lyapunov exponents from small data sets
- Fractal system as represented by singularity function
- YET ANOTHER CHAOTIC ATTRACTOR
- Analysis of fractional differential equations