Related papers: Similarity Between Two Dynamical Systems
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
Quantum mechanics of a general one dimensional dissipative system investigated by it's coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a…
In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is…
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system…
In this article, we compare the dynamics of the shift map and its induced counterpart on the hyperspace of the shift space. We show that many of the properties of induced shift map can be easily demonstrated by appropriate sequences of…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
We study a harmonic system coupled to chain of first neighbor interacting oscillators. After deriving the exact dynamics of the system, we prove that one can effectively describe the exact dynamics by considering a suitable shorter chain.…
We consider a graph theoretic approach to the performance and robustness of a platoon of vehicles, where each vehicle communicates with its $k$-nearest neighbors. In particular, we quantify the platoon's stability margin, robustness to…
In this survey, we study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the…
Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…
Working notes on setting up approximate dynamical systems and nonlinear eigenvalue problems, here embedded within the theory of complex nonlinear dynamics. Computations parallel those of linear quantum theory except that we use functional…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
Here, we develop the exact dynamics of the central spin model, modeling a finite-bath open quantum system. Particularly, two different types of interactions are investigated between the system and the bath: Heisenberg interaction with…