Biomedical subjects

Kevin Wood

Publications and source records attributed to Kevin Wood.

4 recordsLinked to original sources

PubMed2006

Critical behavior and synchronization of discrete stochastic phase-coupled oscillators.

Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean-field limit, the model exhibits a supercritical Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition that we characterize numerically using finite-size scaling analysis. In particular, we explicitly rule out multistability and show that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents beta and nu, a lower critical dimension dlc=2, and an upper critical dimension duc=4.

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PubMed2006

Noise-induced oscillatory behavior in field-dependent relaxational dynamics.

By considering inertial effects in a field-dependent relaxational model, we show that noise may induce collective oscillatory dynamics. In agreement with the recently introduced idea of noise-induced multistability, we show that there is a region in parameter space where such behavior depends on the initial condition. Moreover, when the coupling term leads to pattern formation by means of a morphological instability a la Swift-Hohenberg, [J. Buceta, M. Ibañes, J. M. Sancho, and K. Lindenberg, Phys. Rev. E 67, 021113 (2003) and K. Wood, J. Buceta, and K. Lindenberg, Phys. Rev. E 73, 022101 (2006)] our numerical simulations reveal that spatio-temporal oscillatory structures develop.

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PubMed2006

Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators.

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents beta and nu, a lower critical dimension d(lc) = 2, and an upper critical dimension d(uc) = 4.

Journal Article↗

PubMed2006

Comprehensive study of pattern formation in relaxational systems.

We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [Phys. Rev. E 69, 011102 (2004)]. We demonstrate that the phase diagrams for these systems are entirely determined by a few geometric properties of the field-dependent relaxational coefficient and the local potential. Numerical simulations support the theoretical predictions.

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