Related papers: A network of phase oscillators as a device for seq…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
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…
Legged locomotion is a challenging task in the field of robotics but a rather simple one in nature. This motivates the use of biological methodologies as solutions to this problem. Central pattern generators are neural networks that are…
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 consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
How can we develop simple yet realistic models of the small neural circuits known as central pattern generators (CPGs), which contribute to generate complex multi-phase locomotion in living animals? In this paper we introduce a new model…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…
Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks.…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…
We present a method for reconstructing resonant interactions in weakly coupled phase oscillator systems from noisy time series. Instead of attempting to recover the full phase equations, which may be non-identifiable in the presence of…
Inspired by Axelrod's model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The…
From rhythmic physiological processes to the collective behaviors of technological and natural networks, coherent phases of interacting oscillators are the foundation of the events' coordination leading a system to behave cooperatively. We…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively.
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…