Related papers: Memory selection and information switching in osci…

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…

There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…

We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…

Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…

Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…

Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural…

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use…

Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…

It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for…

While information processing in complex systems can be described in abstract, general terms, there are cases in which the relation between these computations and the physical substrate of the underlying system is itself of interest.…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.

Oscillatory behavior is ubiquitous in many natural and engineered systems, often emerging through self-regulating mechanisms. In this paper, we address the challenge of stabilizing a desired oscillatory pattern in a networked system where…

Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small…

Considering a network of dissipative quantum harmonic oscillators we deduce and analyze the optimum topologies which are able to store, for the largest period of time, a quantum superposition previously prepared in one of the network…

In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…