Related papers: Coarse non-wandering sets and their filtration

Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…

A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering…

This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…

We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…

We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental…

We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…

This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to…

Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…

The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…

We investigate the non-uniqueness of weak solutions of the Quantum-Hydrodynamic system. This form of ill-posedness is related to the change of the number of connected components of the support of the position density (called nodal domains)…

Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical…

This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…

We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

Many transitional wall-bounded shear flows are characterised by the coexistence in state-space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of…

Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes…

Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this…