dorsal/arxiv
View SchemaSynchronisation in Coupled Sine Circle Maps
| Authors | Nandini Chatterjee, Neelima Gupte |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9510001 |
| URL | https://arxiv.org/abs/patt-sol/9510001 |
| DOI | 10.1103/PhysRevE.53.4457 |
Abstract
We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behaviour over a substantial range of parameter space. We have also extended the analysis to higher spatial periods with similar results. Numerical simulations for various temporal periods of the synchronized solution, reveal that the entire structure of the Arnold tongues and the devil's staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice. Our formalism should be useful in the study of spatially periodic behaviour in other coupled map lattices.
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"abstract": "We study the spatially synchronized and temporally periodic solutions of a\n1-d lattice of coupled sine circle maps. We carry out an analytic stability\nanalysis of this spatially synchronized and temporally periodic case and obtain\nthe stability matrix in a neat block diagonal form. We find spatially\nsynchronized behaviour over a substantial range of parameter space. We have\nalso extended the analysis to higher spatial periods with similar results.\nNumerical simulations for various temporal periods of the synchronized\nsolution, reveal that the entire structure of the Arnold tongues and the\ndevil\u0027s staircase seen in the case of the single circle map can also be\nobserved for the synchronized coupled sine circle map lattice. Our formalism\nshould be useful in the study of spatially periodic behaviour in other coupled\nmap lattices.",
"arxiv_id": "patt-sol/9510001",
"authors": [
"Nandini Chatterjee",
"Neelima Gupte"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.53.4457",
"title": "Synchronisation in Coupled Sine Circle Maps",
"url": "https://arxiv.org/abs/patt-sol/9510001"
},
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