Spatial disorder and pattern formation in lattices of coupled bistable elements

Physica D: Nonlinear Phenomena

Volumn 100, Issue 3-4, 1997, Pages 330-342

  Nekorkin, V I ^a   Makarov, V A ^a   Kazantsev, V B ^a   Velarde, M G ^b  

^a LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Bistable oscillators; Lattices; Patterns; Reaction diffusion; Spatial disorder

Indexed keywords

EID: 0001138458     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00202-3     Document Type: Article

References (19)

1. C.M. Bowden, M. Ciftan and J.R. Robl, eds., Optical Bistability (Plenum, New York, 1981).
2. A. Hohl, H.J.C. Van der Linden and R. Roy, Scalling laws for dynamical hysteresis in a multidimensional laser system, Phys. Rev. lett. 74 (1995) 2220-2223.
3. J.D. Murray, Mathematical Biology (Springer, Berlin, 1993).
4. A.T. Winfree, Varieties of spiral wave behaviour: An experimentalists approach to the theory of excitable media, Chaos 1 (1991) 303-334.
5. J.P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987) 556-572.
6. B. Zinner, Stability of travelling wavefronts for the discrete Nagumo equation, SIAM J. Math. Anal. 22 (1991) 1016-1020.
7. B. Zinner, Existence of travelling wavefront solutions for the discrete Nagumo equation, J. Diff. Eqns. 96 (1992) 1-27.
8. T. Erneux and G. Nicolis, Propagating waves in discrete bistable reaction-diffusion systems, Physica D 67 (1993) 237-244.
9. A.R.A. Anderson and B.D. Sleeman, Wave front propagation and its failure in coupled systems of discrete bistable cells modelled by FitzHugh-Nagumo dynamics, Int. J. Bifurc. and Chaos 5 (1995) 63-74.
10. R.S. Mackay and J.-A. Sepulchre, Multistability in networks of weakly coupled bistable units, Physica D 82 (1995) 243-254.
11. A.-D. Defontaines, Y. Pomeau and B. Rostand, Chain of coupled bistable oscillators: A model, Physica D 46 (1990) 201-216.
12. V.I. Nekorkin and V.A. Makarov, Spatial chaos in a chain of coupled bistable oscillators, Phys. Rev. Lett. 74 (1995) 4819-4822.
13. V.I. Nekorkin, V.A. Makarov and M.G. Velarde, Spatial disorder and waves in a ring chain of bistable oscillators, Int. J. Bifurc. and Chaos (1996), to appear.
14. V.S. Afraimovich, L.Y. Glebsky and V.I. Nekorkin, Stability of stationary states and topological spatial chaos in multidimensional lattice dynamical systems, Int. J. Random Comput. Dyn. 2 (1994) 287-303.
15. D. Zwillinger, Handbook of Differential Equations (Academic Press, London, 1989).
16. V.S. Afraimovich, V.I. Nekorkin, G.V. Osipov and V.D. Shalfeev, Stability, Structures and Chaos in Nonlinear Synchronization Networks (World Scientific, Singapore, 1995).
17. V.S. Afraimovich, A.B. Ezersky, M.I. Rabinovich, M.A. Shereshevsky and A.L. Zhelenznyak, Dynamical description of spatial disorder, Physica D 58 (1992) 331-338.
18. J. Rinzel, in: Some mathematical Questions in Biology. VII. Lectures on Mathematics in the Life Sciences, Vol. 8 (American Mathematical Society, Providence, RI, 1976) 125-164.
19. R. Horn and U. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1986).