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On chaotic models with hidden attractors in fractional calculus above power law
- Source :
- Chaos, Solitons & Fractals. 127:24-30
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- Researchers around the world are still wondering about the real origin and causes of hidden oscillating regimes and hidden attractors exhibited by some non-linear complex models. Such models are characterized by a dynamic with a basin of attraction that does not contain neighborhoods of equilibrium points. In this paper, we show that hidden oscillating regimes and hidden attractors can also exist in systems resulting from a combination with fractional differentiation. We apply a fractional derivative with Mittag–Leffler Kernel to a dynamical system with an exponential non-linear term and analyzed the resulting model both analytically and numerically. The combined model, which has no equilibrium points is however shown to display complex oscillating trajectories that culminate in chaos. Numerical simulations show some bifurcation dynamics with respect to the derivative order β and prove that the observed chaotic behavior persists as β varies. These observations made here allow us to say that the fractional model under study belongs to the category of systems with hidden oscillations.
- Subjects :
- Equilibrium point
General Mathematics
Applied Mathematics
Chaotic
General Physics and Astronomy
Statistical and Nonlinear Physics
Dynamical system
01 natural sciences
010305 fluids & plasmas
Fractional calculus
Exponential function
Kernel (image processing)
0103 physical sciences
Attractor
Statistical physics
010301 acoustics
Bifurcation
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 127
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........ee48e7237a758868d88568bd98f64f36