Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators

Nonlinearity

Volumn 10, Issue 3, 1997, Pages 679-713

  Sepulchre, Jacques Alexandre ^a   MacKay, Robert S ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001573592     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/3/006     Document Type: Article

References (27)

1. Aubry S 1997 Breathers in nonlinear lattices: existence, linear stability and quantization Physica D at press
2. Aubry S and Abramovici G 1990 Chaotic trajectories in the standard map: the concept of anti-integrability Physica D 43 199-219
3. Baesens C, Kim S and MacKay R S 1997 Localized modes on coherent structures, in preparation
4. Baesens C and MacKay R S 1994 Improved proof of existence of chaotic polaronic and bipolaronic states for the adiabatic Holstein model and generalizations Nonlinearity 7 59-84
5. Baesens C and MacKay R S 1997 Exponential localisation of linear response in networks with exponentially decaying coupling Nonlinearity submitted
6. Bambusi D 1996 Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators Nonlinearity 9 433-57
7. Campbell D K and Peyrard M 1990 Chaos and order in nonintegrable model field theories Chaos ed D K Campbell (New York: AIP) pp 305-34.
8. Dauxois T, Peyrard M and Bishop AR 1993 Dynamics and thermodynamics of a nonlinear model for DNA denaturation Phys. Rev. E 47 684-95
9. Dauxois T, Peyrard M and Willis C R 1992 Localized breather-like solution in a discrete Klein-Gordon model and application to DNA Physica 57D 267-82
10. Defontaines A D, Pomeau Y and Rostand B 1990 Chain of coupled bistable oscillators: a model Physica 46D 201-16
11. Dunford D and Schwartz J T 1958 Linear Operators; Part I: General Theory (New York: Interscience)
12. Flach S 1995 Existence of localized excitations in nonlinear Hamiltonian lattices Phys. Rev. E 51 1503-7
13. Flach S, Kladko K and MacKay R S 1997 Energy threshold for breathers in one-, two- and three-dimensional lattices Phys. Rev. Lett. at press
14. Flach S and Willis C R 1993 Localized excitations in a discrete Klein-Gordon system Phys. Lett. A 181 232-8
15. Floria L M, Marín J L, Martínez P J, Falo F and Aubry S 1995 Energy localization in the dynamics of a Josephson junction ladder Preprint
16. Hale J K 1969 Ordinary Differential Equations (New York: American Press)
17. Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer)
18. Lang S 1967 Introduction to Differentiable Manifolds, 3rd edn (New York: Interscience)
19. Livi R, Spicci M and MacKay R S 1997 Breathers on a diatomic FPU chain Commun. Math. Phys. submitted
20. MacKay R S 1996 Dynamics of networks: features which persist from the uncoupled limit Stochastic and Spatial Structures of Dynamical Systems ed S J van Strien and S M Verduyn Lunel (Amsterdam: North-Holland) pp 81-104
21. MacKay R S and Aubry S 1994 Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators Nonlinearity 7 1623-43
22. MacKay R S and Sepulchre J-A 1995 Multistability in networks of weakly coupled bistable units Physica D 82 243-54
23. Marín J and Aubry S 1995 Breathers in nonlinear lattices: numerical calculation from the anticontinuous limit Preprint
24. Nekorkin V I and Makarov V A 1995 Spatial chaos in a chain of coupled bistable oscillators Phys. Rev. Lett. 74 4819-22
25. Sepulchre J A and Babloyantz A 1991 Spatio-temporal patterns and network computation Self-Organization, Emerging Properties and Learning (ARW Series) ed A Babloyantz (New York: Plenum) pp 1-20
26. Takeno S, Kisoda K and Sievers A J 1988 Intrinsic localized vibrational modes in anharmonic crystals Prog. Theor. Phys. Suppl. 94 242-69
27. Vakakis A, Nayfeh T and King M 1993 A multiple-scales analysis of nonlinear, localized modes in a cyclic periodic system ASME J. Appl. Mech. 93-APM-35