Related papers: Transitivity in CR-Dynamical Systems
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
This paper explores the properties of adaptive systems with closed-loop reference models. Using additional design freedom available in closed-loop reference models, we design new adaptive controllers that are (a) stable, and (b) have…
We introduce dynamical systems $(X,G)$ with closed relations $G$ on compact metric spaces $X$ and discuss different types of minimality of such dynamical systems, all of them generalizing minimal dynamical systems $(X,f)$ with continuous…
The purpose of the article is to derive equations that determine the trajectory of a non-conservative natural system in configuration space in non-stationary external fields. A theorem on the change in the kinetic energy of the system is…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant--length…
Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
In co-manipulative continuum robots (CCRs), multiple continuum arms cooperate by grasping a common flexible object, forming a closed-chain deformable mechanical system. The closed-chain coupling induces strong dynamic interactions and…
In this paper, we investigate the dynamical behavior of a two dimensional shift $X_G$ (generated by a two dimensional graph $G=(\mathcal{H},\mathcal{V})$) using the adjacency matrices of the generating graph $G$. In particular, we…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using…
Behavior trees represent a hierarchical and modular way of combining several low-level control policies into a high-level task-switching policy. Hybrid dynamical systems can also be seen in terms of task switching between different…