2010 |
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| 2. | Shrimali, Manish Dev; Sharan, Rangoli; Prasad, Awadhesh; Ramaswamy, Ram Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity Journal Article Physics Letters, Section A: General, Atomic and Solid State Physics, 374 (26), pp. 2636–2639, 2010, ISSN: 03759601. Abstract | Links | BibTeX | Tags: Coupled maps, Delay coupling, Synchronization @article{Shrimali2010, title = {Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity}, author = {Manish Dev Shrimali and Rangoli Sharan and Awadhesh Prasad and Ram Ramaswamy}, url = {https://ramramaswamy.org/papers/129.pdf}, doi = {10.1016/j.physleta.2010.04.048}, issn = {03759601}, year = {2010}, date = {2010-01-01}, journal = {Physics Letters, Section A: General, Atomic and Solid State Physics}, volume = {374}, number = {26}, pages = {2636–2639}, abstract = {The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes-termed anomalous behaviour-has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors. textcopyright 2010 Elsevier B.V.}, keywords = {Coupled maps, Delay coupling, Synchronization}, pubstate = {published}, tppubtype = {article} } The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes-termed anomalous behaviour-has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors. textcopyright 2010 Elsevier B.V. |
1995 |
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| 1. | P M Gade, Cerdeira H; Ramaswamy, R Coupled maps on trees Journal Article Physical Review E, 52 (3), pp. 2478–2485, 1995. Abstract | Links | BibTeX | Tags: Coupled map lattice, Coupled maps @article{Gade1995, title = {Coupled maps on trees}, author = {P M Gade, H Cerdeira and R Ramaswamy }, url = {https://link.aps.org/doi/10.1103/PhysRevE.52.2478}, doi = {10.1103/PhysRevE.52.2478}, year = {1995}, date = {1995-09-01}, journal = {Physical Review E}, volume = {52}, number = {3}, pages = {2478–2485}, abstract = {We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. Since the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to achieve. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatiotemporal structures. We find that a mean-field-like treatment is valid on this (effectively infinite dimensional) lattice.}, keywords = {Coupled map lattice, Coupled maps}, pubstate = {published}, tppubtype = {article} } We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. Since the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to achieve. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatiotemporal structures. We find that a mean-field-like treatment is valid on this (effectively infinite dimensional) lattice. |