Stable synchronised states of coupled Tchebyscheff maps

Details Stable synchronised states of coupled Tchebyscheff maps Stable synchronised states of coupled Tchebyscheff maps

2001-10-05

arxiv.org/abs/nlin/0110007v2

Physica D172 (2002) 88-102

Nonlinear Sciences

Chaotic Dynamics

18 pages, postscript figures incorporated into the text; acknowledgements added

Scientific paper

10.1016/S0167-2789(02)00624-3

Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding analytic expressions for a number of periodic states and determining their linear stability. Numerical evidence is given for nonlinear stability of these states, and also the presence of exponentially slow dynamics for some ranges of the parameter. These results indicate that a theory of particle physics based on coupled map lattices must specify strong physical arguments for any choice of initial conditions, and explain how stochastic quantisation is obtained in the many stable parameter regions.

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