Related papers: A Network of Oscillators for Retrieving Phase Info…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
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,…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
Oscillator networks represent a promising technology for unconventional computing and artificial intelligence. Thus far, these systems have primarily been demonstrated in small-scale implementations, such as Ising Machines for solving…
We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains…
In complex networks, interactions between multiple agents give rise to an array of intricate global dynamics, ranging from synchronization to cluster formations. Decoding the connectivity structure as well as the types of interactions from…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
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…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…
We investigate the existence of an optimal interplay between the natural frequencies of a group chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase…