Related papers: Dynamical system analysis in descending dark energ…
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
We generalize the time-variable dark energy scalar field $\Phi$ model ($\Phi$CDM) to nonflat space. We show that even in the space-curvature-dominated epoch the scalar field solution is a time-dependent fixed point or attractor, with scalar…
In this paper we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of $f(R)$-theories. We apply the dynamical system analysis to…
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The…
In the present paper, the effects of viscous dark matter are analysed within the $\Lambda$CDM model. Here we consider bulk viscosity through the Israel-Stewart theory approach, leading to an effective pressure term in the continuity…
This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…
We explore the interaction between dark matter and curvature-driven dark energy within viable $f(R)$ gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as…
We study the autonomous system for a scalar-tensor model of dark energy with non-minimal coupling to curvature and non-minimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios…
Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the…
This paper presents a non-linear stability analysis for dc-microgrids in both, interconnected mode and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient…
We investigate an interacting dark energy model which allows for the kinetic term of the scalar field to couple to dark matter via a power-law interaction. The model is characterised by scaling solutions at early times, which are of high…
A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…
We consider a dynamical approach to the cosmological constant. There is a scalar field with a potential whose minimum occurs at a generic, but negative, value for the vacuum energy, and it has a non-standard kinetic term whose coefficient…
We perform a detailed phase-space analysis of various phantom cosmological models, where the dark energy sector interacts with the dark matter one. We examine whether there exist late-time scaling attractors, corresponding to an…
We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the…
The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a…
The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent…
The oscillating scenario of route to Lambda was recently proposed by us arXiv:0704.1651 as an alternative to a cosmological constant in a explanation of the current accelerating universe. In this scenario phantom scalar field conformally…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
We present a cosmological analysis of an exponential $f(Q)$ gravity model, within the dynamical systems formalism. Following the method introduced by B\"ohmer \textit{et al} [Universe \textbf{9} no.4, 166 (2023)], the modified Friedmann…