Complutense University Library

Spatial disorder and pattern formation in lattices of coupled bistable elements


Makarov, Valeri A. and Nekorkin, Vladimir I. and Kazantsev, V.B. and Velarde, Manuel G. (1997) Spatial disorder and pattern formation in lattices of coupled bistable elements. Physica D-Nonlinear Phenomena, 100 (3-4 ). p. 330. ISSN 0167-2789

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


The spatio-temporal dynamics of discrete lattices of coupled bistable elements is considered. It is shown that both regular and chaotic spatial field distributions can be realized depending on parameter values and initial conditions. For illustration we provide results for two lattice systems: the FitzHugh-Nagumo model and a network of coupled bistable oscillators. For the latter we also prove the existence of phase clusters, with phase locking of elements in each cluster

Item Type:Article
Uncontrolled Keywords:Spatial disorder; Patterns; Bistable oscillators; Reaction-diffusion; Lattices ;Discrete nagumo equation; Systems; Propagation; Oscillators; Failure; Cells; Chain
Subjects:Sciences > Computer science > Operating systems
ID Code:17071

C.M. Bowden, M. Ciftan, J.R. Robl (Eds.), Optical Bistability, Plenum, New York (1981)

A. Hohl, H.J.C. Van der Linden, R. Roy Scalling laws for dynamical hysteresis in a multidimensional laser system Phys. Rev. lett., 74 (1995), pp. 2220–2223

J.D. Murray Mathematical Biology Springer, Berlin (1993)

A.T. Winfree Varieties of spiral wave behaviour: An experimentalists approach to the theory of excitable media Chaos, 1 (1991), pp. 303–334

J.P. Keener Propagation and its failure in coupled systems of discrete excitable cells SIAM J. Math. Appl. Math., 47 (1987), pp. 556–572

B. Zinner Stability of travelling wavefronts for the discrete Nagumo equation SIAM J. Math. Anal., 22 (1991), pp. 1016–1020

B. Zinner Existence of travelling wavefront solutions for the discrete Nagumo equation J. Diff. Eqns., 96 (1992), pp. 1–27

T. Erneux, G. Nicolis Propagating waves in discrete bistable reaction-diffusion systems Physica D, 67 (1993), pp. 237–244

A.R.A. Anderson, 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), pp. 63–74

R.S. Mackay, J.-A. Sepulchre Multistability in networks of weakly coupled bistable units Physica D, 82 (1995), pp. 243–254

A.-D. Defontaines, Y. Pomeau, B. Rostand Chain of coupled bistable oscillators: A model Physica D, 46 (1990), pp. 201–216

V.I. Nekorkin, V.A. Makarov Spatial chaos in a chain of coupled bistable oscillators Phys. Rev. Lett., 74 (1995), pp. 4819–4822

V.I. Nekorkin, V.A. Makarov, M.G. Velarde Spatial disorder and waves in a ring chain of bistable oscillators Int. J. Bifurc. and Chaos (1996) to appear

V.S. Afraimovich, L.Y. Glebsky, V.I. Nekorkin Stability of stationary states and topological spatial chaos in multidimensional lattice dynamical systems Int. J. Random Comput. Dyn., 2 (1994), pp. 287–303

D. Zwillinger Handbook of Differential Equations Academic Press, London (1989)

V.S. Afraimovich, V.I. Nekorkin, G.V. Osipov, V.D. Shalfeev Stability, Structures and Chaos in Nonlinear Synchronization Networks World Scientific, Singapore (1995)

V.S. Afraimovich, A.B. Ezersky, M.I. Rabinovich, M.A. Shereshevsky, A.L. Zhelenznyak Dynamical description of spatial disorder Physica D, 58 (1992), pp. 331–338

J. Rinzel Some mathematical Questions in Biology. VII, Lectures on Mathematics in the Life Sciences, Vol. 8, American Mathematical Society, Providence, RI (1976), pp. 125–164

R. Horn, U. Johnson Matrix Analysis Cambridge University Press, Cambridge (1986)

Deposited On:13 Nov 2012 10:16
Last Modified:28 Jun 2016 14:42

Repository Staff Only: item control page