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Heterogeneous stochastic neuronal networks


We present results from studies of networks of coupled neuronal units. Units are considered as oscillatory, excitabie and chaotic. In the talk we will concentrate on the influence of noise in the collective dynamics of the network, on effects of network-disorder and -correlations, and on modifications arising from the interaction of several distinct populations of stochastic neurons. For all these topics paradigmatic models for phases of the neurons are introduced and will be investigated. Outgoing from the stochastic dynamics of the ensemble of neurons, we formulate nonlinear balance equations for the order parameters of the composite network. Afterward, we study them by bifurcation theory and obtain dependencies on the noise intensity, strength of disorder/heterogeneity and of correlations. Computer simulations support the findings, but show also the limitations of the made approximations in certain cases as will be discussed in the talk.

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B. Sonnenschein, L. Schimansky-Geier, Phys. Rev. E 88, 052111 (2013): Approximate solution to the stochastic Kuramoto model.

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B. Sonnenschein, T. K. DM. Peron, F.A. Rodrigues, J. Kurths, and L. Schimansky-Geier , Phys.l Rev. E 91, 062910 (2015): Collective dynamics in two populations of noisy oscillators with asymmetric interactions.

B. Sonnenschein, T.K.D.M. Peron, F. A. Rodrigues, J. Kurths, and L. Schimansky-Geier, Europ. Phys. Journ. B 87 182 (2014): Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations.

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