Nonlinear analysis of stretch-twist-fold (STF) flow

Nonlinear Dynamics

Volumn 72, Issue 3, 2013, Pages 581-590

  Aqeel, Muhammad ^a   Yue, Bao Zeng ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Chaos; Local behavior; Lyapunov exponent; Poincar map; Power spectrum; Stretch twist fold flow

Indexed keywords

CHAOTIC DYNAMICAL SYSTEMS; FLUID PARTICLE MOTIONS; INITIAL CONDITIONS; LOCAL BEHAVIOR; LYAPUNOV EXPONENT; NUMERICAL CALCULATION; POINCARE; STRETCH-TWIST-FOLD FLOW;

CHAOS THEORY; DIFFERENTIAL EQUATIONS; ELECTROMAGNETIC FIELD EFFECTS; LYAPUNOV FUNCTIONS; MAGNETIC FIELDS; NONLINEAR ANALYSIS; POWER SPECTRUM; SPACECRAFT PROPULSION;

LYAPUNOV METHODS;

EID: 84880701018     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0736-0     Document Type: Article

References (32)

1. Liu, L.; Su, Y.C.: A modified Lorenz system. Int. J. Nonlinear Sci. Numer. Simul. 7, 187-190 (2006)
2. Zeraoulia, E.: Analysis of a new three-dimensional quadratic chaotic system. Radioengineering 17, 9-13 (2008)
3. Alsafasfeh, Q.H.; Al-Arni, M.S.: A new chaotic behavior from Lorenz and Rossler systems and its electronic circuit implementation. Circuits Syst. 2, 101-105 (2011)
4. Yongjian, L.: Analysis of global dynamics in an unusual 3D chaotic system. Nonlinear Dyn. 70, 2203-2212 (2012)
5. Cleary, P.W.: Lyapunov exponents as a measure of the size of chaotic region. J. Math. Phys. 30, 689-695 (1989)
6. Wenbo, L.; Guanrong, C.: Dynamical analysis of a chaotic system with double-scroll chaotic attractors. Int. J. Bifurc. Chaos 14, 971-999 (2004)
7. Alligood, K.T.; Sauer, T.D.; Yorke, J.A.: CHAOS: An Introduction to Dynamical System. Springer, New York (2000)
8. Lorenz, E.N.: Deterministic nonperiodic flow. J. At. Sci. 20, 130-141 (1963)
9. Rossler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397-398 (1976)
10. Tianshou, Z.; Yun, T.: Chen's attractor exists. Int. J. Bifurc. Chaos 9, 3167-3177 (2004)
11. Liangqiang, Z.; Fangqi, C.: Sil'nikov chaos of the Liu system. Chaos 18, 1-5 (2008)
12. Bajer, K.; Moffatt, H.K.; Nex, F.H.: Steady confined stokes flows with chaotic streamlines. In: Moffatt, H.K.; Tsinober, A. (eds.) Topological Fluid Mechanics. Proceedings of the IUTAM Symposium, Technical University of Denmark, pp. 459-466. Cambridge University Press, Cambridge (1990)
13. Atefeh, G.: Nonlinear analysis of human gait signals. Int. J. Inf. Eng. Electron. Bus. 2, 15-21 (2012)
14. Qin, G.; Junhai, M.: Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn. 58, 209-216 (2009)
15. Yue, B.Z.; Wang, Z.: Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment. Chin. Sci. Bull. 51, 2425-2431 (2006)
16. Richard, E.A.; Van, E.; Micheal, T.R.; William, J.M.D.; Joseph, H.: A nonlinear dynamics approach to human movement. J. Appl. Biomech. 20, 396-420 (2004)
17. Li, R.; Xu, B.; Zhang, H.: Dynamic feature analysis of space electrodynamics tether system. J. Vib. Shock 27, 36-40 (2008)
18. Phipps, C.R.; Luke, J.R.; Lippert, T.; Hauer, M.; Wokaun, A.: Micro propulsion using a laser ablation jet. J. Propuls. Power 20, 1000-1011 (2004)
19. Childress, S.; Gilbert, A.D.: Stretch, Twist, Fold: The Fast Dynamo. Springer, Berlin (1995)
20. Moffat, H.K.: Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press, Cambridge (1978)
21. Domber, T.; Frisch, U.; Greene, J.M.: Chaotic stream lines in the ABC flow. J. Fluid Mech. 167, 353-391 (1986)
22. Beloshapkin, V.V.; Chernikov, A.A.; Netonzon, M.Y.: Chaotic stremalines in pre-turbulent states. Nature 337, 133-137 (1988)
23. Vainshtein, S.I.; Zel'dovich, Y.A.B.: Origin of magnetic fields in astrophysics (turbulent "dynamo" mechanisms). Sov. Phys. Usp. 15, 159-172 (1972)
24. Moffatt, H.K.; Proctor, M.R.E.: Topological constraints associated with fast dynamo action. J. Fluid Mech. 154, 493-507 (1985)
25. Bajer, K.; Moffatt, H.K.: On a class of steady confined stokes flows with chaotic streamlines. J. Fluid Mech. 212, 337-363 (1990)
26. Bajer, K.: Flow kinematics and magnetic equilibria. PhD thesis, Cambridge University Press, Cambridge (1989)
27. Bao, J.; Yang, Q.: Complex dynamics in the stretch-twist-fold flow. Nonlinear Dyn. 61, 773-781 (2010)
28. Bao, J.; Yang, Q.: A new method to find homoclinic and heteroclinic orbits. Appl. Math. Comput. 217, 6526-6540 (2011)
29. Strogatz, S.H.: Non Linear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview, Cambridge (2000)
30. Greene, J.M.; Kim, J.S.: The calculation of Lyapunov spectra. Physica D 24, 213-225 (1987)
31. Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285-317 (1985)
32. Wolfram, J.; Holger, H.: Some consideration on Poincare maps for chaotic flows. J. Phys. A, Math. Gen. 33, 163-170 (2000)