Related papers: Periodic orbits in the Ott-Antonsen manifold
We study a particular return map for a class of low dimensional chaotic models called Kolmogorov Lorenz systems, which received an elegant general Hamiltonian description and includes also the famous Lorenz63 case, from the viewpoint of…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
The Kuramoto model is a paradigm for studying oscillator networks with interplay between coupling tending towards synchronization, and heterogeneity in the oscillator population driving away from synchrony. In continuum versions of this…
We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial…
The coexistence of coherent and incoherent domains, namely the appearance of chimera states, is being studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the…
We consider an array of non-locally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problem-dependent critical value so-called event collisions occur. This paper classifies…
We find chimera states with respect to amplitude dynamics in a network of Stuart-Landau oscillators. These partially coherent and partially incoherent spatio-temporal patterns appear due to the interplay of nonlocal network topology and…
The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressive genes in bacteria…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations…
We study the onset of collective oscillations at low temperature in a three-dimensional spin model with non-reciprocal short-range interactions. Performing numerical simulations of the model, the presence of a continuous phase transition to…
The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the…
We investigate the transition from synchronized to chimera states in a ring of non-locally coupled phase oscillators. Our focus is on the intermediate defect states, where solitary waves in the phase gradient profile travel at a constant…
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and…