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An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the phenomenon of resonance may appear. We give a sufficient condition on the…
Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This…
The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time…
The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic…
Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the…
The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time…
Multiple organs in a living system respond to environmental changes, and the signals from the organs regulate the physiological environment. Inspired by this biological feedback, we propose a simple autonomous system of active rotators to…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…
Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood…