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Many real oscillators are coupled to other oscillators, and the coupling can affect the response of the oscillators to stimuli. We investigate phase-response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the… (More)

We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function. Various quantities of the partially locked states are computed through a self-consistency argument and the values show good… (More)

We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use… (More)

We investigate the effects of axonal time delay when the neuronal oscillators are coupled by sparse and random connections. Using phase-reduced models with general coupling functions, we show that a small fraction of connections with time delay can destabilize synchronous states and induce near-regular wave states. An order parameter is introduced to… (More)

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control parameter in this study. It is found that distance-dependent time delays induce various patterns including traveling… (More)

We study the dynamics of randomly coupled oscillators when interactions between oscillators are time delayed due to the finite and constant speed of coupling signals. Numerical simulations show that the time delays, proportional to the Euclidean distances between interacting oscillators, can induce near regular waves in addition to near in-phase synchronous… (More)

We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike pinwheels, (anti)spirals with phase-randomized cores, and antiferro patterns embedded in (anti)spirals. We consider the… (More)

The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of… (More)

The effect of coupling strength inhomogeneity on the synchronization of identical oscillators is investigated. Through simulations and analysis of phase-reduced models, it is shown that the mean value of coupling function and the degree of inhomogeneity in the total of coupling strength to the each oscillator cooperate to stabilize incoherent states. Under… (More)

Brain anatomical connectivity is one of the main factors influencing information flow among the brain areas [1] and phase lead/lag relationship between oscillations of brain areas is known to be related to the information flow [2,3]. In this study, we analyze the network effect on the phases of coupled oscillators using Kuramoto model and obtain analytical… (More)