Complex and transitive synchronization in a frustrated system of calling frogs

Aihara, Ikkyu; Takeda, Ryo; Mizumoto, Takeshi; Otsuka, Takuma; Takahashi, Tôru; Okuno, Hiroshi G.; Aihara, Kazuyuki

doi:10.1103/physreve.83.031913

Cited by 41 publications

(105 citation statements)

References 16 publications

(34 reference statements)

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“…In the following lemma, we give sufficient conditions for asymptotic stability of the origin of (18), (19). In particular, we prove that under some mild assumptions, there always exists a region S 1 in the parameter space (predictor gain j and total time-delay s), such that if ðj; sÞ 2 S 1 , then the system (15)- (17) anticipates the dynamics (6)- (8). Moreover, it is also proved that the region S 1 is bounded by a unimodal function uðjÞ defined on some set J & R.…”

Section: -4mentioning

confidence: 98%

“…For instance, in biology, it is well known that thousands of fireflies light up simultaneously 7 and that groups of Japanese tree frogs (Hyla japonica) may show synchronous behavior in their calls. 8 In medicine and neuroscience, clusters of synchronized pacemaker neurons regulating our heartbeat, 9 synchronized neurons in the olfactory bulb that allow us to detect and distinguish between odors, 10 and our circadian rhythm, which is synchronized to the 24-h day-night cycle 11,12 are clear examples. In engineering, one of the most commonly cited examples of network synchronization is the problem of coordinated motion of individual mobile agents.…”

Section: Introductionmentioning

confidence: 99%

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Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Murguía

Fey

Nijmeijer

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. This manuscript focuses on controlled synchronization of identical nonlinear systems interacting on networks with general topologies and interconnected through predictorbased diffusive dynamic couplings. The systems are said to be diffusively coupled, if they interact through weighted differences of the form c(y j À y i ) with some positive constant c called the coupling strength and y i , y j denoting the outputs of the ith and jth systems. An important element of our control scheme is the use of a communication network. Network communication is necessary in the study of synchronization to transmit and receive measurement and control data among the systems. Because of the time needed to transmit data over the network, the use of networked communication to exchange information results in unavoidable time-delays. This networked-induced delays are undesirable because they may lead to the loss of synchrony. Hence, when studying synchronization among dynamical systems with networked communication, it is important to design control algorithms which are robust with respect to time-delays. The results presented here follow the same research line as Refs. 1 and 2, where sufficient conditions for synchronization of diffusively interconnected nonlinear systems with and without time-delays are derived. In order to derive their results, the authors assume that the individual systems are semipassive 3 with respect to the coupling variable y i , and their corresponding internal dynamics have some desired stability properties (convergent internal dynamics 4 ). In particular, in Ref. 2, the authors study the problem of network synchronization of diffusively timedelayed coupled semipassive systems. They prove that under some mild assumptions, there always exists a region S in the parameter space (coupling strength c versus time-delay s), such that if ðc; sÞ 2 S, the systems synchronize. Nevertheless, it is important to note that for this class of systems, once the network topology is specified, the re...

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Section: -4mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Murguía

Fey

Nijmeijer

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…For instance, in biology, it is well known that thousands of fireflies light up simultaneously, see Strogatz [2003], and that groups of Japanese tree frogs (Hyla japonica) may show synchronous behavior in their calls, see Aihara et al [2011]. In medicine and neuroscience, clusters of synchronized pacemaker neurons regulating our heartbeats, Peskin [1975], and our circadian rhythm, which is synchronized to the 24-h day-night cycle, Czeisler et al [1980], are clear examples.…”

Section: Introductionmentioning

confidence: 98%

Synchronization in Cartesian-Product Networks of Time-Delay Coupled Systems

et al. 2015

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We present a theoretical result about synchronization in Cartesian-product networks of coupled semipassive systems interconnected through diffusive time-delay couplings. First, for two diffusively time-delay coupled systems, we give sufficient conditions that guarantee the existence of a region S * in the parameter space (coupling strength vs. time delay), such that if these parameters belong to the region, the two coupled systems synchronize. Then, using this region S * and the spectral properties of the Cartesian-product, we derive a method to predict the values of coupling strength and time-delay for which diffusive timedelay coupled systems on Cartesian-product networks synchronize. The obtained theoretical results are experimentally validated using an experimental setup built around electronic circuit realizations of the Hindmarsh-Rose neuron model.

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“…In biophysics, in an attempt to construct a hexagonal lattice of repressing genes, socalled dynamical frustrated states have been found to appear, where the temporal evolution is chaotic, even if there is no built-in frustration [7]. In mathematical ecology, experimental results for a three-frogs system, in which a frog was joined into a pair calling out of phase, have been given [8]. Specifically, both the triphase and the 1:2 antiphase synchronization, including switching between the two states, have been reported.…”

Section: Introductionmentioning

confidence: 99%

Frustration in the Pattern Formation of Polysyllabic Words

Hayata

2017

Front. Phys.

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A novel frustrated system is given for the analysis of (m + 1)-syllabled vocal sounds for languages with the m-vowel system, where the varieties of vowels are assumed to be m (m ≥ 2). The necessary and sufficient condition for observing the sound frustration is that the configuration of m vowels in an m-syllabled word has a preference for the "repulsive" type, in which there is no duplication of an identical vowel. For languages that meet this requirement, no (m + 1)-syllabled word can in principle select the present type because at most m different vowels are available and consequently the duplicated use of an identical vowel is inevitable. For languages showing a preference for the "attractive" type, where an identical vowel aggregates in a word, there arises no such conflict. In this paper, we first elucidate for Arabic with m = 3 how to deal with the conflicting situation, where a statistical approach based on the chi-square testing is employed. In addition to the conventional three-vowel system, analyses are made also for Russian, where a polysyllabic word contains both a stressed and an indeterminate vowel. Through the statistical analyses the selection scheme for quadrisyllabic configurations is found to be strongly dependent on the parts of speech as well as the gender of nouns. In order to emphasize the relevance to the sound model of binary oppositions, analyzed results of Greek verbs are also given.

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Complex and transitive synchronization in a frustrated system of calling frogs

Cited by 41 publications

References 16 publications

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Synchronization in Cartesian-Product Networks of Time-Delay Coupled Systems

Frustration in the Pattern Formation of Polysyllabic Words

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