Related papers: Dynamical systems of M\"obius transformation: real…
We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own mathematical models and algorithms designed to accomplish its objectives. A…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We introduce an adic (Bratteli-Vershik) dynamical system based on a diagram whose path counts from the root are the Delannoy numbers. We identify the ergodic invariant measures, prove total ergodicity for each of them, and initiate the…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
Continuing work begun in a previous paper, we study the real dynamics of a family of plane birational maps. This time we consider a parameter range where the real and complex dynamics are different. We show in particular that for one…
A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over…
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
The dynamics of the family of maps $\displaystyle{f_{\alpha, \beta, \gamma, \delta}(z)=\frac{\alpha z + \beta}{\gamma z^2 +\delta z}}$ in complex plane is investigated computationally. This dynamical system $z_{n+1}=f_{\alpha, \beta,…
This paper is part of a program to understand the parameter spaces of dynamical systems generated by meromorphic functions with finitely many singular values. We give a full description of the parameter space for a specific family based on…
In this article, we combine complex-analytic and arithmetic tools to study the preperiodic points of one-dimensional complex dynamical systems. We show that for any fixed complex numbers a and b, and any integer d at least 2, the set of…
Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable…
We analyze the cosmological solutions of $f(T,B)$ gravity using dynamical system analysis where $T$ is the torsion scalar and $B$ be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we…
Relations between points in the phase space are central to the study of topological dynamical systems. Since many of these relations share common properties, it is natural to study them within a unified framework. To this end, we introduce…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…