We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an all-to-all connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.

How and why the presence of a person directly affects the perception and action of another person is a phenomenon that has been approached in a limited and piecemeal fashion within psychology. This kind of diffuse strategy has failed to capture the jointness of perception and action within and between people. In contradistinction, the authors offer a perspective that retains both integrally social features (e.g., involves interaction) and yet adequately exploits the current state of knowledge regarding the ecological properties of perception–action, while at the same time drawing on aspects of dynamic systems theory. In this article the authors review the best attempts to examine how one individual affects another’s perceptions and actions in the emergence of a social unit of action. Two important approaches, the individual-level and cognitive dynamics approaches, have yielded insights that derive in significant degree from principles of ecological psychology and/or dynamical systems theory. Prototypic of the individual-level approach is a focus on what can be perceived by coactors with the aim of uncovering how the dispositional qualities (affordances) of another person are informationally specified during social interaction. In contrast, the cognitive dynamics approach simulates dynamical characteristics of cognition and psychological influence with the aim of uncovering how cooperative interaction emerges out of its component parts. The authors argue that these approaches involve, respectively, insufficient mutuality and insufficient embodiment. Consequently, a social synergy perspective is discussed that approaches the problem of socially cooperative interaction at the relational, nonreductive level, using novel methods to examine how social perception and action emerge through self-organizing processes.

This paper introduces a method for the coordination of individual action within a group of robots that have to accomplish a common task, gathering energy in a dynamic environment and transferring this energy to a nest. Each individual behavioral pattern is driven by an internal neural rhythm generator exhibiting quasi-periodic oscillations. The paper describes the implementation of this generator, its influence on the dynamics of artificial recurrent neural networks controlling the robots, and the synchronization of internal rhythms with differing frequencies in a group of situated and embodied robots. Synchronization is achieved either by environmental stimuli or even by self-organizing processes solely based on local interactions within a robot population of up to 150 robots. The proposed experimental methodology is used as a bottom-up approach and starting point for answering the question about the complexity required at the individual level to generate sophisticated behavioral patterns at the group level.

Abstract — Fireflies exhibit a fascinating phenomenon of spontaneous synchronization that occurs in nature: at dawn, they gather on trees and synchronize progressively without relying on a central entity. The present article 1 reviews this process by looking at experiments that were made on fireflies and the mathematical model of Mirollo and Strogatz [1], which provides key rules to obtaining a synchronized network in a decentralized manner. This model is then applied to wireless ad hoc networks. To properly apply this model with an accuracy limited only to the propagation delay, a novel synchronization scheme, which is derived from the original firefly synchronization principle, is presented, and simulation results are given. I.

Many observers have marveled at the beauty of the synchronous flashing of fireflies that has an almost hypnotic effect. In this paper we consider the issue of evolving two-dimensional cellular automata as well as random boolean networks to solve the firefly synchronization task. The task was successfully solved by means of cellular programming based co-evolution performing computations in a completely local manner, each cell having access only to its immediate neighbor's states. An FPGA-based...

Abstract — In this article spontaneous synchronization observed in nature is applied to self-organized wireless networks. In South-East Asia huge swarms of fireflies emit light flashes in perfect synchrony. The underlying principle of this firefly synchronization scheme is reviewed and challenges related to the implementation in ad hoc networks are addressed. In particular, the effects of transmission delays and the constraint that a node cannot receive and transmit at the same time are studied. I.

Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring. I.

The delicate interplay between knot theory and dynamical systems is surveyed. Numerous bridges between these elds allow us to apply dynamical perspectives (entropy, "chaotic") to knot theory, as well as knot-theoretic perspectives (cablings, "wild") to dynamical phenomena and bifurcations thereof. This intricate relationship has opened new doors in the study of ODE models of physical systems, while conversely yielding interesting topological objects from dynamical flows.

We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a noisy system with many highly correlated elements there will be a strong effect of error synchronization. These postulates appear to be damaging for quantum computers.

Self-organised synchronisation is a common phenomenon observed in many natural and artificial systems: simple coupling rules at the level of the individual components of the system result in an overall coherent behaviour. Owing to these properties, synchronisation appears particularly interesting for swarm robotics systems, as it allows for robust temporal coordination of the group while minimising the complexity of the individual controllers. The goal of the experiments presented in this paper is the study of self-organising synchronisation for robots that present an individual periodic behaviour. In order to design the robot controllers, we make use of artificial evolution, which proves to be capable of synthesising minimal synchronisation strategies based on the dynamical coupling between robots and environment. The obtained results are analysed under a dynamical system perspective, which allows us to uncover the evolved mechanisms and to predict the scalability properties of the self-organising synchronisation with respect to varying group size.