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Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial…
In this manuscript, a silent resonator neuron is coupled with a spiking integrator neuron through the gap junction, when the coupled neurons are of different types of excitability and none of the coupled neurons exhibit mixed mode…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…
This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
In this paper we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number of oscillators N…
It is shown that long term behavior of two connected Integrate- and- Fire neurons with excitatory synapses is determined by some fixed-points. In the case of equal synaptic weights four different dynamic phases are found. Between these…
Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…
Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
We investigate the dynamics of a deterministic self-propelled particle endowed with coherent memory. We evidence experimentally and numerically that it exhibits several stable free states. The system is composed of a self-propelled drop…
To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…