Local Stable or Unstable Regions in 2-Dimensional Chaotic Forms: Examples and Simulations

• Authors: C. Skiadas
• Languages of publication: EN

Abstracts

EN

We analyze 2-}dimensional chaotic forms resulting from very simple systems based on two chaotic characteristics that is rotation and parallel movement or translation in geometric terms. Reflection is another alternative, along with rotation, for several interesting chaotic formations. Rotation and translation are very common types of movements in the world around us. Chaotic or non-chaotic forms arise from these two main generators. The rotation-translation chaotic case presented is based on the theory we analyzed in the book and in the paper. An overview of the chaotic flows in rotation-translation is given. There is observed the presence of chaos when discrete rotation-translation equation forms are introduced. In such cases the continuous equations analogue of the discrete cases is useful. Characteristic cases and illustrations of chaotic attractors and forms are analyzed and simulated. The analysis of chaotic forms and attractors of the models presented is given along with an exploration of the characteristic or equilibrium points. Applications in the fields of astronomy-astrophysics (galaxies), chaotic advection (the sink problem) and Von Karman streets are presented.

Keywords

EN

95.10.Fh; 47.52.+j; 05.45.Pq; 98.62.-g; 47.32.C-; 47.32.Ef; 45.20.dc

Discipline

• 47.32.Ef: Rotating and swirling flows
• 47.32.C-: Vortex dynamics
• 05.45.Pq: Numerical simulations of chaotic systems
• 47.52.+j: Chaos in fluid dynamics(see also 05.45.-a Nonlinear dynamics and chaos in Statistical physics, thermodynamics, and nonlinear dynamical systems)
• 95.10.Fh: Chaotic dynamics(see also 05.45.-a Nonlinear dynamics and chaos)
• 98.62.-g: Characteristics and properties of external galaxies and extragalactic objects(for the Milky Way, see 98.35.-a)
• 45.20.dc: Rotational dynamics

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 6
• Pages: 1082-1086

Dates

published

2013-12

Contributors

author

C. Skiadas

• ManLab, Technical University of Crete, Greece

References

• [1] R.M. May, Nature 261, 459 (1976)
• [2] E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)
• [3] M. Hénon, C. Heiles, Astron. J. 69, 73 (1964)
• [4] K. Ikeda, Opt. Commun. 30, 257 (1979)
• [5] H. Aref, Ann. Rev. Fluid Mech. 15, 345 (1983)
• [6] C.H. Skiadas, C. Skiadas, Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms, CRC/Taylor and Francis, Boca Raton (FL) 2008
• [7] C.H. Skiadas, C. Skiadas, Int. J. Bifurcation Chaos 21, 3023 (2011)
• [8] C.H. Skiadas, 'Chaotic dynamics in simple rotation-reflection models,' in: Int. Workshop on Galaxies and Chaos: Theory and Observations, Academy of Athens, Astronomy Research Center, Athens 2002
• [9] C.H. Skiadas, in: Topics on Chaotic Systems, World Sci., Singapore 2009, p. 309
• [10] C.H. Skiadas, in: Recent Advances in Stochastic Modeling and Data Analysis, World Sci., Singapore, 2007, p. 287

Identifiers

DOI

10.12693/APhysPolA.124.1082