Chaos in temporarily destabilized regular systems with the slow passage effect

Chaos, Solitons and Fractals

Volumn 27, Issue 2, 2006, Pages 395-403

  Perc, Matjaž ^a   Marhl, Marko ^a  

^a UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTROL THEORY; GEOPHYSICS; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; POLYNOMIALS;

CHAOS CONTROL ALGORITHMS; CHAOTIC SYSTEM; DESTABILIZED REGULAR SYSTEMS; SLOW PASSAGE EFFECT;

CHAOS THEORY;

EID: 22844441607     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.03.045     Document Type: Article

References (61)

1. E. Ott, C. Grebogi, and J.A. Yorke Controlling chaos Phys Rev Lett 64 1990 1196 1199
2. K. Pyragas Continuous control of chaos by self-controlling feedback Phys Lett A 170 1992 421 428
3. T. Shinbrot, C. Grebogi, E. Ott, and J.A. Yorke Using small perturbations to control chaos Nature 363 1993 411 417
4. T. Kapitaniak Chaos for engineers: theory, applications and control 1998 Springer Berlin
5. G. Chen, and X. Dong From chaos to order: methodologies, perspectives and applications 1998 World Scientific Singapore
6. S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancini, and D. Maza The control of chaos: theory and applications Phys Rep 329 2000 103 197
7. A. Garfinkel, M.L. Spano, W.L. Ditto, and J.N. Weiss Controlling cardiac chaos Science 257 1992 1230 1235
8. S.J. Schiff, K. Jerger, D.H. Duong, T. Chang, M.L. Spano, and W.L. Ditto Controlling chaos in the brain Nature 370 1994 615 620
9. W. Yang, M. Ding, A.J. Mandell, and E. Ott Preserving chaos: control strategies to preserve complex dynamics with potential relevance to biological disorders Phys Rev E 51 1995 102 110
10. H.D.I. Abarbanel Analysis of observed chaotic data 1996 Springer New York
11. I.B. Schwartz, and I.T. Georgiou Instant chaos and hysteresis in coupled linear-nonlinear oscillators Phys Lett A 242 1998 307 312
12. I.T. Georgiou, and I.B. Schwartz Dynamics of large scale coupled structural mechanical systems: a singular perturbation proper orthogonal decomposition approach SIAM J Appl Math 59 1999 1178 1207
13. L.M. Pecora, and T.L. Carroll Synchronization in chaotic systems Phys Rev Lett 64 1990 821 824
14. S. Hayes, C. Grebogi, and E. Ott Communicating with chaos Phys Rev Lett 70 1993 3031 3034
15. J.H. Peng, E.J. Ding, M. Ding, and W. Yang Synchronizing hyperchaos with a scalar transmitted signal Phys Rev Lett 76 1996 904 907
16. G.D. VanWiggeren, and R. Roy Communication with chaotic lasers Science 279 1998 1198 1200
17. S.Q. Zhu, X. Lu, X.F. Chen, K.S. Thornburg, G.D. VanWiggeren, and R. Roy General synchronization of chaos in a system of two non-identical lasers Chin Phys 9 2000 337 341
18. T. Kapitaniak Continuous control and synchronization in chaotic systems Chaos, Solitons & Fractals 6 1995 237 244
19. J. Brindley, T. Kapitaniak, and L. Kocarev Controlling chaos by chaos in geophysical systems Geophys Res Lett 22 1995 1257 1260
20. G. Chen, and D. Lai Feedback control of Lyapunov exponents for discrete-time dynamical systems Int J Bifurcat Chaos 6 1996 1341 1349
21. G. Chen, and D. Lai Making a dynamical system chaotic: feedback control of Lyapunov exponents for discrete-time dynamical systems IEEE Trans Circuits Syst 44 1997 250 253
22. G. Chen, and D. Lai Feedback anticontrol of discrete chaos Int J Bifurcat Chaos 8 1998 1585 1590
23. I. Triandaf, and I.B. Schwartz Tracking sustained chaos: a segmentation method Phys Rev E 62 2000 3529 3534
24. X.F. Wang, G. Chen, and X. Yu Anticontrol of chaos in continuous systems via time-delay feedback Chaos 10 2000 771 779
25. K. Konishi Making chaotic behavior in a damped linear harmonic oscillator Phys Lett A 284 2001 85 90
26. M. Chen, and Z. Han An iteration method for chaotifying and controlling dynamical systems Int J Bifurcat Chaos 12 2002 1173 1180
27. L. Yang, Z. Liu, and G. Chen Chaotifying a continuous-time system via impulsive input Int J Bifurcat Chaos 12 2002 1121 1128
28. G. Chen, L. Yang, and Z. Liu Anticontrol of chaos in continuous-time system IEICE Trans Fundament E85-A 2002 1333 1335
29. S. Codreanu Desynchronization and chaotification of nonlinear dynamical systems Chaos, Solitons & Fractals 13 2002 839 843
30. G. Chen, and L. Yang Chaotifying a continuous-time system near a stable limit cycle Chaos, Solitons & Fractals 15 2003 245 253
31. C. Li, and G. Chen On the Marotto-Li-Chen theorem and its application to chaotification of multi-dimensional discrete dynamical systems Chaos, Solitons & Fractals 18 2003 807 817
32. C. Li On super-chaotifying discrete dynamical systems Chaos, Solitons & Fractals 21 2004 855 861
33. M.-F. Danca Chaotifying discontinuous dynamical systems via time-delay feedback algorithm Int J Bifurcat Chaos 7 2004 2321 2339
34. H.-K. Chen, and C.-I. Lee Anti-control of chaos in rigid body motion Chaos, Solitons & Fractals 21 2004 957 965
35. K. Starkov, and G. Chen Chaotification of polynomial continuous-time systems and rational normal forms Chaos, Solitons & Fractals 22 2004 849 856
36. A. Nejshtadt Asymptotic investigation of the loss of stability by an equilibrium as a pair of eigenvalues slowly cross the imaginary axis Usp Math Nauk 40 1985 190 191
37. J. Rinzel, and M. Baer Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on fluctuations Biophys J 54 1988 551 555
38. S.M. Baer, T. Erneux, and J. Rinzel The slow passage through a Hopf bifurcation: delay, memory effects, and resonances SIAM J Appl Math 49 1989 55 71
39. L. Holden, and T. Erneux Slow passage through a Hopf bifurcation: from oscillatory to steady state solutions SIAM J Appl Math 53 1993 1045 1058
40. L. Holden, and T. Erneux Understanding bursting oscillations as periodic slow passages through bifurcation and limit points J Math Biol 31 1993 351 365
41. E.M. Izhikevich Neural excitability spiking and bursting Int J Bifurcat Chaos 10 2000 1171 1266
42. E.M. Izhikevich Synchronisation of Elliptic Bursters SIAM Rev 43 2001 315 344
43. M. Perc, and M. Marhl Different types of bursting calcium oscillations in non-excitable cells Chaos, Solitons & Fractals 18 2003 759 773
44. M. Perc, and M. Marhl Synchronization of regular and chaotic oscillations: the role of local divergence and the slow passage effect. A case study on calcium oscillations Int J Bifurcat Chaos 14 2004 2735 2751
45. A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano Determining Lyapunov exponents from a time series Physica D 16 1985 285 317
46. S. Boccaletti, and F.T. Arecchi Adaptive-control of chaos Europhys Lett 31 1995 127 132
47. S. Boccaletti, and F.T. Arecchi Adaptive recognition and control of chaos Physica D 96 1996 9 16
48. M. Marhl, T. Haberichter, M. Brumen, and R. Heinrich Complex calcium oscillations and the role of mitochondria and cytosolic proteins BioSystems 57 2000 75 86
49. J. Rinzel Bursting oscillations in an excitable membrane model Lecture Notes in Mathematic 1151 1985 Springer Berlin
50. E. Doedel, A. Champneys, T. Fairgrieve, and Y. Kuznetsov AUTO97: continuation and bifurcation software for ordinary differential equations 1997 Concordia University Montreal
51. M. Perc, and M. Marhl Detecting and controlling unstable periodic orbits that are not part of a chaotic attractor Phys Rev E 70 2004 016204
52. T. Haberichter, M. Marhl, and R. Heinrich Birhythmicity, trirhythmicity and chaos in bursting calcium oscillations Biophys Chem 90 2001 17 30
53. J. Zhang, C.W. Wang, A. Blaszcyzk, J.A. Grifo, J. Ozil, and E. Haberman Electrical activation and in vitro development of human oocytes that fail to fertilize after intracytoplasmic sperm injection Fertility and Sterility 72 1999 509 512
54. G. Temes, J. Lantos, and B. Torok Possibility of brain recovery after electrically induced cardiac arrest and reanimation in dogs Acta Physiol Hung 70 1987 93 103
55. J.L. Beyer, R.D. Weiner, and M.D. Glenn Electroconvulsive therapy: a programmed text 1998 American Psychiatric Press Washington
56. P. Torricelli, M. Fini, G. Giavaresi, V. Cane, and R. Giardino In vitro evaluation of the effects of electromagnetic fields used for bone healing Electro Magnetobiol 17 1998 335 342
57. D.M. Ciombor, G. Lester, R.K. Aaron, P. Neame, and B. Caterson Low frequency EMF regulates chondrocyte differentiation and expression of matrix proteins J Orthopaed Res 20 2002 40 50
58. R.K. Aaron, S. Wang, and D.M. Ciombor Upregulation of basal TGF beta (l) levels by EMF coincident with chondrogenesis-implications for skeletal repair and tissue engineering J Orthopaed Res 20 2002 233 240
59. M. De Mattei, M. Pasello, A. Pellati, G. Stabellini, L. Massari, and D. Gemmati Effects of electromagnetic fields on proteoglycan metabolism of bovine articular cartilage explants Connect Tissue Res 44 2003 154 159
60. M. De Mattei, A. Pellati, M. Pasello, A. Ongaro, S. Setti, and L. Massari Effects of physical stimulation with electromagnetic field and insulin growth factor-I treatment on proteoglycan synthesis of bovine articular cartilage Osteoarthr Cartilage 12 2004 793 800
61. Electroconvulsive therapy, http://www.psycom.net/depression.central.ect.html.