Shear-induced chaos

Nonlinearity

Volumn 21, Issue 5, 2008, Pages 899-922

  Lin, Kevin K ^a,b   Young, Lai Sang ^a  

^a NEW YORK UNIVERSITY   (United States)

^b The University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43049129652     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/5/002     Document Type: Article

References (39)

1. Arnold L 1998 Random Dynamical Systems (Berlin: Springer)
2. Arnold L, Sri Namachchivaya N and Schenk-Hoppé K R 1996 Toward an understanding of stochastic Hopf Bifurcation: a case study Int. J. Bifurcation Chaos 6 1947-75
3. Auslender E I and Mil'shten G N 1982 Asymptotic expansions of the Liapunov index for linear stochastic systems with small noise J. Appl. Math. Mech. 46 358-65
4. Baxendale P H 1994 A stochastic Hopf bifurcation Probab. Theory Relat. Fields 581-616
5. Baxendale P H 2003 Lyapunov exponents and stability for the stochastic Duffing-van der Pol oscillator IUTAM Symp. on Nonlinear Stochastic Dynamics, Solid Mech. Appl. 110 125-35
6. Baxendale P H 2004 Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation Stochastic Process. Appl. 113 235-72
7. Baxendale P H 2002 Lyapunov exponents and resonance for small periodic and random perturbations of a conservative linear system Stochastic Dyn. 2 49-66
8. Baxendale P H and Goukasian L 2002 Lyapunov exponents for small random perturbations of Hamiltonian systems Ann. Probab. 30 101-34
9. Benedicks M and Carleson L 1991 The dynamics of the Hénon map Ann. Math. 133 73-169
10. Broer H, Simó C and Tatjer J C 1998 Towards global models near homoclinic tangencies of dissipative diffeomorphisms Nonlinearity 11 667-770
11. Guckenheimer J 1974 Isochrons and phaseless sets J. Theor. Biol. 1 259-73
12. Guckenheimer J and Holmes P 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Berlin: Springer)
13. Guckenheimer J, Weschelberger M and Young L-S 2006 Chaotic attractors of relaxation oscillators Nonlinearity 19 701-20
14. Haller G and Poje A C 1998 Finite time transport in aperiodic flows Physica D 119 352-80
15. Jakobson M 1981 Absolutely continuous invariant measures for one-parameter families of one-dimensional maps Commun. Math. Phys. 81 39-88
16. Kifer Yu 1986 Ergodic Theory of Random Transformations (Basle: Birkhäuser)
17. Kunita H 1990 Stochastic Flows and Stochastic Differential Equations (Cambridge: Cambridge University Press)
18. Ledrappier F and Young L-S 1985 The metric entropy of diffeomorphisms Ann. Math. 122 509-74
19. Levi M 1981 Qualitative analysis of periodically forced relaxation oscillations Mem. Am. Math. Soc. 214 1-147
20. Lin K K, Shea-Brown E and Young L-S 2006 Reliable and unreliable dynamics in driven coupled oscillators Preprint arXiv: nlin/0608021v1
21. Lin K K, Shea-Brown E and Young L-S 2007 Reliability of coupled oscillators: I. Two-oscillator systems Preprint arXiv: 0708.3061v2
22. Mora L and Viana M 1993 Abundance of strange attractors Acta Math. 171 1-71
23. Sri Namachchivaya N 2007 The asymptotic stability of a weakly perturbed 2-dimensional non-Hamiltonian system private communication
24. Newhouse S 1980 Lectures on Dynamical Systems (Progress in Mathametics vol 8) (Basle: Birkhäuser) pp 1-114
25. Oksasoglu A and Wang Q 2005 Strange attractors in periodically-kicked Chua's circuit Int. J. Bifurcation Chaos 16 83-98
26. Palis J and Takens F 1993 Hyperbolicity & Sensitive Chaotic Dynamics at Homoclinic Bifurcations (Cambridge Studies in Advanced Mathematics vol 35) (Cambridge: Cambridge University Press)
27. Pesin Ja B 1977 Characteristic Lyapunov exponents and smooth ergodic theory Russ. Math. Surv. 32.4 55-114
28. Pinsky M and Wihstutz V 1998 Lyapunov exponents of nilpotent It systems Stochastics 25 43-57
29. Pugh C and Shub M 2000 Stable ergodicity and julienne quasi-conformality J. Eur. Math. Soc. 2 1-52
30. Ruelle D 1979 Ergodic theory of differentiable dynamical systems Publ. Math. Inst. Hautes tud. Sci. 50 27-58
31. Schenk-Hoppé K R 1996 Bifurcation scenarios of the noisy Duffing-van der Pol oscillator Nonlinear Dyn. 11 255-74
32. Taylor D and Holmes P 1998 Simple models for excitable and oscillatory neural networks J. Math. Biol. 37 419-46
33. van der Pol B and van der Mark J 1927 Frequency demultiplication Nature 120 363-4
34. Wang Q and Young L-S 2001 Strange attractors with one direction of instability Commun. Math. Phys. 218 1-97
35. Wang Q and Young L-S 2002 From invariant curves to strange attractors Commun. Math. Phys. 225 275-304
36. Wang Q and Young L-S 2003 Strange attractors in periodically-kicked limit cycles and Hopf bifurcations Commun. Math. Phys. 240 509-29
37. Wang Q and Young L-S 2008 Toward a theory of rank one attractors Ann. Math. 167 349-480
38. Winfree A 2000 The Geometry of Biological Time 2nd edn (Berlin: Springer)
39. Zaslavsky G 1978 The simplest case of a strange attractor Phys. Lett. A 69 145-7