Related papers: Ghost states underlying spatial and temporal patte…

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…

Ghost fields have reemerged in a handful of phenomenologically motivated cosmological and particle physics scenarios, and most recently in a cyclic mechanism to address the fine-tuning of gauge couplings in the standard model. We study the…

Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global…

A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…

N-body systems characterized by inverse square attractive forces may display a self similar collapse known as the gravo-thermal catastrophe. In star clusters, collapse is halted by binary stars, and a large fraction of Milky Way clusters…

Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including…

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…

Nonlinear systems driven by noise and periodic forces with more than one frequency exhibit the phenomenon of Ghost Stochastic Resonance (GSR) found in a wide and disparate variety of fields ranging from biology to geophysics. The common…

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L.…

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely…

We study a correspondence between $f(R)$ model of gravity and a phenomenological kind of dark energy (DE), which is known as QCD ghost dark energy. Since this kind of dark energy is not stable in the context of Einsteinian theory of gravity…

In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is…

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

The study of dynamical systems has long focused on the characterization of their asymptotic dynamics such as fixed points, limit cycles and other types of attractors and how these invariant sets change their properties as systems parameters…

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…

We study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduces nonlinearity into an otherwise linear system. We…

Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric…

In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most…

Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…