Related papers: Topological phase transition in the periodically f…
We investigate a generalized Kuramoto phase-oscillator model with Hebb-like couplings that evolve according to a stochastic differential equation on various topologies. Numerical simulations show that even with identical oscillators, there…
Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the…
We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving…
Short-time dynamics of many-body systems may exhibit non-analytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder new critical…
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…
We propose a scenario for the formation of localized turbulent spots in transition flows, which is known as resulting from the subcritical character of the transition. We show that it is not necessary to add 'by hand" a term of random noise…
In this note we show that for the Kuramoto model defined in a simple undirected graph it is possible to decide which nodes form the core of the network. The set of core-nodes is defined by its relevance to the phase synchronisation process.
We analyze the evolution of scalar and gauge fields during first order phase transitions and show how the Kibble mechanism for the formation of topological defects emerges from the underlying dynamics, paying particular attention to…
Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary…
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders - chiral and random types - to explore the interplay between topology and disorder. By tracking…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two…
We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from…
Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with…
A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…