Analytic Determination of the Critical Coupling for Oscillators in a Ring

We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major clusters, which merge to form a larger one of all oscillators at the stage of complete synchronization. We are able to locate these four oscillators as well as the size of major clusters in the vicinity of the stage of full synchronization which we show to depend only on the set of initial frequencies. Using the method presented here, we are able to obtain an analytic form of the critical coupling, at which the complete synchronization state occurs.Comment: 5 pages and 3 figure

Nonlocal synchronization in nearest neighbour coupled oscillators

We investigate a system of nearest neighbor coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbor coupling. The power spectra of nonadjacent oscillators show that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighboring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbors in space. It is also shown that when a direct coupling between non-neighbors oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbors coincide

Nonstandard Farey sequences in a realistic diode map

We study a realistic coupled-map system, modelling a p-i-n diode structure. As we vary the parameter corresponding to the (scaled) external potential in the model the dynamics goes through an exchange of stability bifurcation and a Hopf bifurcation. When the parameter is increased further, we find evidence of a sequence of mode-locked windows embedded in the quasi-periodic motion. These periodic attractors can be ordered according to a Farey tree that is generated between two parent fractions 2/7 and 2/8, where 2/8 implies two distinct coexisting attractors with ρ=¼, and the correct structure is obtained only when we use the parent fraction 2/8. So, unlike a regular Farey tree, here numerator and denominator of the Farey fractions need not be relative primes. We also checked that the positions and widths of these windows exhibit well-defined power law scaling. When the potential is increased further, the Farey windows still provide a "skeleton" for the dynamics, and within each window there is a host of other interesting dynamical features, including multiple forward and reverse Feigenbaum trees

Transition to complete synchronization in phase coupled oscillators with nearest neighbours coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.Comment: 6 pages, 4 figures, to appear in CHAO

Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated to switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases

Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that they posses different characteristics, depending on the section of the boundary of the SR where the solutions appear. We study the birth of these solutions and how they evolve when {K} increases, and determine the diagram of solutions in phase space.Comment: 8 pages, 10 figure

Parameter and coupling estimation in small groups of Izhikevich neurons

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems which produce these data, appropriate analysis tools are needed}. The Kalman filter is a {frequently used} technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the Unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. {I}n this work, we test whether the UKF can also reconstruct the connectivity of {small groups of} coupled neurons when their links are either electrical or chemical {synapses}. {In particular, w}e consider Izhikevich neurons, and aim to infer which neurons influence each other, considering {simulated spike trains as the experimental observations used by the UKF}. First, we {verify} that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and}} demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and {temporally evolving} networks. {Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system

Study of the image of the tourist region of Lisbon

A indústria turística mundial registou um crescimento anual constante e encontrava-se em franca expansão até março de 2020, quando foi fortemente afetada pela pandemia Covid-19. Acredita-se que para a reinvenção e reforma do setor se terá de investir fortemente na criação e gestão da perceção dos turistas sobre a imagem dos destinos turísticos. Tendo em vista este contexto, o presente estudo objetiva analisar a imagem da região de Lisboa através da utilização de User Generated Content (UGC). A metodologia utilizada tem como base de análise três componentes de interações do turista com o destino: imagem Designativa, Estimativa e Prescritiva. Foram utilizados 51 mil reviews do ano de 2019, em inglês, contendo opinião de turistas de 131 nacionalidades sobre a região turística de Lisboa. Os resultados revelam que Lisboa tem uma imagem caracterizada por reviews positivos e oferecem novos conhecimentos sobre a gestão da imagem do destino.info:eu-repo/semantics/publishedVersio