Synchronicity is a useful abstraction in many sensor network applications. Communication scheduling, coordinated duty cycling, and time synchronization can make use of a synchronicity primitive that achieves a tight alignment of individual nodes ’ firing phases. In this paper we present the Reachback Firefly Algorithm (RFA), a decentralized synchronicity algorithm implemented on TinyOS-based motes. Our algorithm is based on a mathematical model that describes how fireflies and neurons spontaneously synchronize. Previous work has assumed idealized nodes and not considered realistic effects of sensor network communication, such as message delays and loss. Our algorithm accounts for these effects by allowing nodes to use delayed information from the past to adjust the future firing phase. We present an evaluation of RFA that proceeds on three fronts. First, we prove the convergence of our algorithm in simple cases and predict the effect of parameter choices. Second, we leverage the TinyOS simulator to investigate the effects of varying parameter choice and network topology. Finally, we present results obtained on an indoor sensor network testbed demonstrating that our algorithm can synchronize sensor network devices to within 100 µsec on a real multi-hop topology with links of varying quality.

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.

Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

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Abstract. Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and I-cells (excitatory and inhibitory cells): The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as “PING ” (Pyramidal-Interneuronal Gamma) rhythms. The PING mechanism requires that the drive II to the I-cells be sufficiently low; the rhythm is lost when II gets too large. This can happen in (at least) two different ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells, and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism

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.

The work of this thesis has focused on creating computational models of developing neurons. Three different but related areas of research have been studied - how cells make connections, what influences the shape of these connections and how neuronal network behaviour can be influenced by local interactions. In order to understand how cells make connections I simulated the dynamics of the neuronal growth cone - a structure which guides the developing axon to its target cells. Results from the first models showed that small interaction effects between structural proteins in the axon called microtubules can significantly alter the rate of axonal elongation and turning. I also simulated the dynamics of growth cone filopodia. The filopodia act as antennae and explore the extracellular environment surrounding the growth cone. This model showed that a reaction-diffusion system based on Turing morphogenesis patterns could account for the dynamic behaviour of filopodia. To find out what influen...

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions. The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of magnitude smaller than periods

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In this article we evaluate an epidemic algorithm for the synchronization of coupled Kuramoto oscillators in complex Peer-to-Peer topologies. The algorithm requires a periodic coupling of nodes to a single random one-hop-neighbor. The strength of the nodes ’ couplings is given as a function of the degrees of both coupling partners. We study the emergence of self-synchronization and the resilience against node failures for different coupling functions and network topologies. For Watts/Strogatz networks, we observe critical behavior suggesting that small-world properties of the underlying topology are crucial for self-synchronization to occur. From simulations on networks under the effect of churn, we draw the conclusion that special coupling functions can be used to enhance synchronization resilience in power-law Peer-to-Peer topologies.