Dresden 2009 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 14: Neuronal and Sensory Systems
BP 14.7: Vortrag
Mittwoch, 25. März 2009, 16:00–16:15, HÜL 186
First order phase transition to criticality by adaptive interactions — •Anna Levina1,2, J. Michael Herrmann1,2,3, and Theo Geisel1,2 — 1BCCN-Göttingen, Bunsenstr. 10, 37073 Göttingen — 2MPI DS, Bunsenstr. 10, 37073 Göttingen — 3University of Edinburgh, 10 Crichton Street, Edinburgh EH8 9AB, U.K.
The concept of self-organized criticality (SOC) describes a variety of phenomena ranging from plate tectonics, the dynamics of granular media to neural avalanches. In all these cases the dynamics is marginally stable and event sizes obey a characteristic power-law distribution. It was previously shown that an extended critical interval can be obtained in a neural network by incorporation of depressive synapses. In the present study we scrutinize a more realistic dynamics for the synaptic interactions that can be considered as the state-of-the-art in computational modeling of synaptic interaction. Interestingly, the more complex model does not exclude an analytical treatment and it shows a type of stationary state consisting of critical and a subcritical phases. The phases are connected by first- or second-order phase transitions in a cusp bifurcation which is implied by the dynamical equations of the underlying biological model. We present exact analytical results supported by extensive numerical simulations. Although presented in the specific context of a neural model, the dynamical structure of our model is of more general interest. It is the first observation of a system that combines a complex classical bifurcation scenario with a robust critical phase. The system may account not only for SOC behavior, but also for various switching effects observed in the brain.