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We consider a generic description of interacting dynamical Dark Energy, characterized by an equation of state with a time dependent coefficient $w(t)$, and which may interact with both radiation and matter. Without referring to any…
The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
We report that under some specific conditions a single qubit model weakly interacting with information environments can be referred to as a quantum classifier. We exploit the additivity and the divisibility properties of the completely…
A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of…
We investigate a quintessence axion model for dynamical dark energy, motivated in part by recent results from the Baryon Acoustic Oscillation (BAO) measurements of the Dark Energy Spectroscopic Instrument (DESI) combined with the cosmic…
As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background…
In this paper we have studied the dynamics of accelerating scenario within the framework of scalar field models possessing a non-canonical kinetic term. In this toy model, the scalar field is allowed to interact with the dark matter…
Dark energy models with tracker properties have gained attention due to the large range of initial conditions leading to the current value of the dark energy density parameter. A well-motivated family of these models are the so-called…
Experimental manipulations perturb the neuronal activity. This phenomenon is manifested in the fMRI response. Dynamic causal model and its variants can model these neuronal responses along with the BOLD responses [1, 2, 3, 4, 5] .…
Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate with dark or grey kink solitons in the presence of localized dissipation. To this end, the 3D Gross-Pitaevskii equation with an additional imaginary…
In this paper, we propose a new approach to study the dark sector of the universe by considering the dark energy as emerging a q-deformed bosonic scalar field which is not only interacting with the dark matter, but also non-minimally…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
We use the linear $\sigma$ model to analyse the dynamics of a disoriented chiral condensate. For idealized boundary conditions appropriate to high energy collisions, the problem can be reduced to a one dimensional one. The evolution of the…
We consider the cosmological dynamics of the cubic Galileon field model interacting with dark matter, where the interaction between the cosmic dark sectors is proportional to Hubble parameter and dark energy density. The background field…
Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…
After about two decades of the first observational papers confirming the accelerated expansion of the universe, we are still facing the question whether the cause of it is a rigid cosmological constant $\Lambda$-term or a mildly evolving…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…