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We present a method to infer the complete connectivity of a network from its stable response dynamics. As a paradigmatic example, we consider networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving. For a given driving condition, measuring the phase differences and the collective(More)
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send(More)
Controlling sensori-motor systems in higher animals or complex robots is a challenging combinatorial problem, because many sensory signals need to be simultaneously coordinated into a broad behavioural spectrum. To rapidly interact with the environment, this control needs to be fast and adaptive. Present robotic solutions operate with limited autonomy and(More)
Irregular dynamics in multidimensional systems is commonly associated with chaos. For infinitely large sparse networks of spiking neurons, mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary(More)
Robust synchronization (phase locking) of power plants and consumers centrally underlies the stable operation of electric power grids. Despite current attempts to control large-scale networks, even their uncontrolled collective dynamics is not fully understood. Here we analyze conditions enabling self-organized synchronization in oscillator networks that(More)
UNLABELLED Hippocampal activity is fundamental for episodic memory formation and consolidation. During phases of rest and sleep, it exhibits sharp-wave/ripple (SPW/R) complexes, which are short episodes of increased activity with superimposed high-frequency oscillations. Simultaneously, spike sequences reflecting previous behavior, such as traversed(More)
Inferring the network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method for inferring the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network(More)
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem—local stability of synchrony—is non-trivial to solve and requires novel methods for its solution. In particular, the discrete mode of pulsed communication(More)
We consider unstable attractors: Milnor attractors A such that, for some neighbourhood U of A, almost all initial conditions leave U . Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e. for open sets of parameter values) in a system modelling biological phenomena, namely in globally coupled oscillators with(More)