James Brody
November 25th, 2008, 12:05 PM
Nets: Tit for Tat
Reciprocity occurs at all levels. Kuramoto survives...
JimB
"Synchronization of coupled demographic oscillators
Tobias Galla (Dated: November 25, 2008)
"Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that synchronization to a common frequency can occur between two such systems, even if they oscillate at different frequencies in the absence of coupling. The power spectra of the separate and the coupled systems are computed within a van Kampen expansion in the inverse system size, and it is found that they exhibit two peaks at separate frequencies at low coupling, but that only one peak is present at large enough coupling strength. We further make predictions on the time behaviour of the phases of the two oscillators, and their phase difference, and confirm the frequency entrainment at sufficiently large coupling. Theoretical results are verified convincingly in numerical simulations."
More at http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.3689v1.pdf
References
Daniels, Bryan C. (2005) Synchronization of globally connected nonlinear oscillators: the rich behavior of the Kuramoto model. Physics Department: Ohio Wesleyan University, Delaware, Ohio. Demo at http://physics.owu.edu/StudentResearch/2005/BryanDaniels/kuramoto.html
Strogatz, S. (2003) Sync: The Emerging Science of Spontaneous Order. NY: Hyperion. (readable, interesting, relevant everywhere! See also Chapter 3 in Brody JF, 2008, Rebellion: Physics to Personal Will, iuniverse.
Reciprocity occurs at all levels. Kuramoto survives...
JimB
"Synchronization of coupled demographic oscillators
Tobias Galla (Dated: November 25, 2008)
"Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that synchronization to a common frequency can occur between two such systems, even if they oscillate at different frequencies in the absence of coupling. The power spectra of the separate and the coupled systems are computed within a van Kampen expansion in the inverse system size, and it is found that they exhibit two peaks at separate frequencies at low coupling, but that only one peak is present at large enough coupling strength. We further make predictions on the time behaviour of the phases of the two oscillators, and their phase difference, and confirm the frequency entrainment at sufficiently large coupling. Theoretical results are verified convincingly in numerical simulations."
More at http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.3689v1.pdf
References
Daniels, Bryan C. (2005) Synchronization of globally connected nonlinear oscillators: the rich behavior of the Kuramoto model. Physics Department: Ohio Wesleyan University, Delaware, Ohio. Demo at http://physics.owu.edu/StudentResearch/2005/BryanDaniels/kuramoto.html
Strogatz, S. (2003) Sync: The Emerging Science of Spontaneous Order. NY: Hyperion. (readable, interesting, relevant everywhere! See also Chapter 3 in Brody JF, 2008, Rebellion: Physics to Personal Will, iuniverse.