Gluing bifurcations in optothermal nonlinear devices

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 5, 1998, Pages 5366-5377

  Herrero, R ^a,b,c   Farjas, J ^a,b,c   Pons, R ^a,b,c   Pi, F ^a,b,c   Orriols, G ^a,b,c  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF GIRONA   (Spain)

^c UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; IRRADIATION; LASER BEAMS; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES; OPTICAL DEVICES; OSCILLATIONS;

GLUING BIFURCATIONS; HOMOCLINICITY; OPTOTHERMAL NONLINEAR DEVICE; SADDLE POINT; TWO LOBED LIMIT CYCLE;

CHAOS THEORY;

EID: 0032075163     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.5366     Document Type: Article

References (35)

1. J. Gukenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
2. P. Gaspard, Physica D 62, 94 (1993).PDNPDT
3. J. Palis and F. Takens, Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations (Cambridge University Press, Cambridge, 1993).
4. L. P. Shil’nikov, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 489 (1994).IJBEE4
5. P. Glendinning, in New Directions in Dynamical Systems, edited by T. Bedford and J. Swift (Cambridge University Press, Cambridge, 1988), p. 120.
6. L. P. Shil’nikov, Math. USSR Sb. 10, 91 (1970).ZZZZZZ
7. For a synthetic review, see A. R. Champneys and Yu. A. Kuznetsov, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 785 (1994), and references therein.IJBEE4
8. P. Coullet, J. M. Gambaudo, and C. Tresser, C. R. Acad. Sci., Ser. I: Math. 299, 253 (1984).CASMEI
9. J. M. Gambaudo, P. A. Glendinning, and C. Tresser, C. R. Acad. Sci., Ser. I: Math. 299, 711 (1984)
10. J. M. GambaudoP. A. GlendinningC. TresserJ. Phys. (France) Lett. 46, 653 (1985).
11. D. Turaev and L. P. Shil’nikov, Sov. Math. Dokl. 34, 397 (1987).ZZZZZZ
12. J. M. Gambaudo, P. A. Glendinning, and C. Tresser, in Instabilities and Nonequilibrium Structures, edited by E. Tirapegui and D. Villarroel (Reidel, Dordrecht, 1987), p. 41.
13. J. M. Gambaudo, P. A. Glendinning, and C. Tresser, Nonlinearity 1, 203 (1988).NONLE5
14. D. V. Lyubimov, A. S. Pikovsky, and M. A. Zaks, Universal Scenarios of Transitions to Chaos via Homoclinic Bifurcations, Math. Phys. Rev. Vol. 8 (Harwood Academic, London, 1989), Pt. 4.
15. J. Coste and N. Peyraud, Phys. Lett. 84A, 17 (1981).PYLAAG
16. Y. Kuramoto and S. Koga, Phys. Lett. 92A, 1 (1982).PYLAAG
17. E. Meron and I. Procaccia, Phys. Rev. A 35, 4008 (1987).PLRAAN
18. A. M. Rucklidge, Physica D 62, 323 (1993).PDNPDT
19. J. I. Rosell, F. Pi, F. Boixader, R. Herrero, J. Farjas, and G. Orriols, Opt. Commun. 82, 162 (1991).OPCOB8
20. R. Herrero, F. Boixader, G. Orriols, J. I. Rosell, and F. Pi, Opt. Commun. 113, 324 (1994).OPCOB8
21. R. Herrero, R. Pons, J. Farjas, F. Pi, and G. Orriols, Phys. Rev. E 53, 5627 (1996).PLEEE8
22. J. I. Rosell, J. Farjas, R. Herrero, F. Pi, and G. Orriols, Physica D 85, 509 (1995).PDNPDT
23. J. Farjas, J. I. Rosell, R. Herrero, R. Pons, F. Pi, and G. Orriols, Physica D 95, 107 (1996).PDNPDT
24. Silicone F600, from Bayer AG.
25. G. Orriols, C. Schmidt-Iglesias, and F. Pi, Opt. Commun. 63, 66 (1987).OPCOB8
26. Gel 0608, from Cargille Lab.
27. M. Bosch and C. Simó, Physica D 62, 217 (1993).PDNPDT
28. L. P. Shil’nikov, Math. USSR Sb. 6, 427 (1968).ZZZZZZ
29. According to definitions given in Ref. 17, the dimensionless parameters describing the system are kj=Dj=1/0.1/1, ηj=1/-9/1, gj=1/0.4/g3, for j=1/2/3, hF=hB=0.5, and cavity mirrors the same as considered in Ref. 17.
30. V. S. Afraimovich and L. P. Shil’nikov, in Nonlinear Dynamics and Turbulence, edited by G. I. Barenblatt, G. Iooss, and D. D. Joseph (Pitman, Boston, 1983), p. 1.
31. The resonant side switching occurs in the degenerate point of a homoclinic bifurcation curve where the saddle point exchanges from negative to positive value and, besides the consequent modification of the homoclinic bifurcation, a cyclic saddle-node bifurcation emerges from it 7.
32. L. P. Shil’nikov, in the russian edition of The Hopf Bifurcation and Its Applications, edited by J. E. Marsden, and M. McCracken (Mir, Moscow, 1980), p. 317.
33. J. M. Gambaudo, I. Procaccia, S. Thomae, and C. Tresser, Phys. Rev. Lett. 57, 925 (1986).PRLTAO
34. Y. S. Fan and T. R. Chay, Phys. Rev. E 51, 1012 (1995).PLEEE8
35. The Γ(10)j symbols in Fig. 77(b) indicate the occurrence of the saddle-node bifurcation while the homoclinic bifurcation takes place displaced to the right at an unknown position.