Related papers: Collective modes of coupled phase oscillators with…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…
We develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations. Collective phase equations describing macroscopic rhythms of the system are derived from Langevin-type…
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…
We investigated the locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in the coupling…
Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Current proofs show that delay coordinates of a given dynamical…
We show that for pulse coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of…
We study numerically the effects of time delay in networks of delay-coupled excitable FitzHugh Nagumo systems with dissipation. The generation of periodic self-sustained oscillations and its threshold are analyzed depending on the…
We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
Collective cell migration lies at the intersection of developmental biology and non-equilibrium physics, where active processes give rise to emergent patterns that are biologically relevant. Here, we investigate dilatational modes--cycles…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the…
Collective modes of bilayered superconducting superlattices (e.g., YBCO) are investigated within the conserving gauge-invariant ladder diagram approximation including both the nearest interlayer single electron tunneling and the…