Related papers: The dependence on the initial states and the trans…

We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…

Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a…

This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…

Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyze several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence…

In this paper, we define B-smooth discontinuous dynamical systems which can be used as models of various processes in mechanics, electronics, biology and medicine. We find sufficient conditions to guarantee the existence of such systems.…

Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that…

In topological dynamics, tame and null systems arise naturally in the study of low-complexity aperiodic behaviour, yet providing concrete and easily testable conditions to establish their existence in a canonical class of systems is often…

This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…

Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…

In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has…

For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…

We construct the set of theories which share the property that the tree-level amplitudes nullify even if both initial and final states contain the same type of particles. The origin of this phenomenon lies in the fact that the reduced…

Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…

Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly…

We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…

The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…

As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…

For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…

In many scenarios, it is natural to model a plant's dynamical behavior using a hybrid dynamical system influenced by exogenous continuous-time inputs. While solution concepts and analytical tools for existence and completeness are well…