相关论文: Switched flow systems: pseudo billiard dynamics

Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…

We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…

Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy…

The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as…

We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…

In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…

In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…

We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…

The singular bifurcations in a dispersive billiard are discussed in terms of symbolic dynamics and is compared to an example of a bifurcation tree in a smooth potential. Possible generalizations to other smooth potentials are discussed.

A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…

We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method…

The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in laboratory. Despite recent developments in modern…

Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…

\textsc{J. Hadamard} studied the geometric properties of geodesic flows on surfaces of negative curvature, thus initiating "Symbolic Dynamics". In this article, we follow the same geometric approach to study the geodesic trajectories of…

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…

The dynamics and deformations of immersed flexible fibers are at the heart of important industrial and biological processes, induce peculiar mechanical and transport properties in the fluids that contain them, and are the basis for novel…

The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…