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Grabow C.,Max Planck Institute for Dynamics and Self-Organization | Grosskinsky S.,University of Warwick | Timme M.,Max Planck Institute for Dynamics and Self-Organization | Timme M.,Bernstein Center for Computational Neuroscience Gottingen | Timme M.,University of Gottingen
European Physical Journal B | Year: 2011

Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times for directed networks with topologies ranging from completely ordered, grid-like, to completely disordered, random, including intermediate, partially disordered topologies. We extend the approach of master stability functions to quantify synchronization times. We find that the synchronization times strongly and systematically depend on the network topology. In particular, at fixed in-degree, stronger topological randomness induces faster synchronization, whereas at fixed path length, synchronization is slowest for intermediate randomness in the small-world regime. Randomly rewiring real-world neural, social and transport networks confirms this picture. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. Source

Greene G.,Ludwig Maximilians University of Munich | Greene G.,Bernstein Center for Computational Neuroscience Munich | Gollisch T.,Bernstein Center for Computational Neuroscience Munich | Gollisch T.,University of Gottingen | And 3 more authors.
Vision Research | Year: 2016

Fixational eye movements can rapidly shift the retinal image, but typically remain unnoticed. We identify and simulate a model mechanism for the suppression of erroneous motion signals under fixational eye movements. This mechanism exploits the non-linearities common to many classes of large retinal ganglion cells in the mammalian retina, and negates the need for extra-retinal signals or explicit gaze information. When tested using natural images undergoing simulated fixational eye movements, our model successfully distinguishes "real world" motion from retinal motion induced by eye movements. In addition, this model suggests a possible explanation for several fixational eye movement related visual illusions such as the Ouchi-Spillmann and "Out-of-focus" illusions. © 2015 Elsevier Ltd. Source

Kriener B.,Norwegian University of Life Sciences | Kriener B.,Max Planck Institute for Dynamics and Self-Organization | Kriener B.,Bernstein Center for Computational Neuroscience Gottingen
Chaos | Year: 2012

Under which conditions can a network of pulse-coupled oscillators sustain stable collective activity states? Previously, it was shown that stability of the simplest pattern conceivable, i.e., global synchrony, in networks of symmetrically pulse-coupled oscillators can be decided in a rigorous mathematical fashion, if interactions either all advance or all retard oscillation phases ("mono-interaction network"). Yet, many real-world networks-for example neuronal circuits-are asymmetric and moreover crucially feature both types of interactions. Here, we study complex networks of excitatory (phase-advancing) and inhibitory (phase-retarding) leaky integrate-and-fire (LIF) oscillators. We show that for small coupling strength, previous results for mono-interaction networks also apply here: pulse time perturbations eventually decay if they are smaller than a transmission delay and if all eigenvalues of the linear stability operator have absolute value smaller or equal to one. In this case, the level of inhibition must typically be significantly stronger than that of excitation to ensure local stability of synchrony. For stronger coupling, however, network synchrony eventually becomes unstable to any finite perturbation, even if inhibition is strong and all eigenvalues of the stability operator are at most unity. This new type of instability occurs when any oscillator, inspite of receiving inhibitory input from the network on average, can by chance receive sufficient excitatory input to fire a pulse before all other pulses in the system are delivered, thus breaking the near-synchronous perturbation pattern. © 2012 American Institute of Physics. Source

Timme M.,Max Planck Institute for Dynamics and Self-Organization | Timme M.,Bernstein Center for Computational Neuroscience Gottingen | Timme M.,University of Gottingen | Casadiego J.,Max Planck Institute for Dynamics and Self-Organization
Journal of Physics A: Mathematical and Theoretical | Year: 2014

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity. © 2014 IOP Publishing Ltd. Source

Effenberger F.,Max Planck Institute for Mathematics in the Sciences | Jost J.,Max Planck Institute for Mathematics in the Sciences | Levina A.,Max Planck Institute for Mathematics in the Sciences | Levina A.,Bernstein Center for Computational Neuroscience Gottingen
PLoS Computational Biology | Year: 2015

Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Here we present an adaptive model of a balanced neuronal network that combines two different types of plasticity, STDP and synaptic scaling. The plasticity rules yield both long-tailed distributions of synaptic weights and firing rates. Simultaneously, a highly connected subnetwork of driver neurons with strong synapses emerges. Coincident spiking activity of several driver cells can evoke population bursts and driver cells have similar dynamical properties as leader neurons found experimentally. Our model allows us to observe the delicate interplay between structural and dynamical properties of the emergent inhomogeneities. It is simple, robust to parameter changes and able to explain a multitude of different experimental findings in one basic network. © 2015 Effenberger et al. Source

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