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The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
We investigate the dynamics of periodic non-autonomous discrete dynamical systems on uniform spaces and topological spaces, focusing on the extension of the classical Auslander-Yorke dichotomy to these settings. We prove various dichotomy…
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a very general form of dichotomy known as…
This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
In this paper we have studied the dynamics of accelerating scenario within the framework of scalar field models possessing a non-canonical kinetic term. In this toy model, the scalar field is allowed to interact with the dark matter…
We introduce the concept of multi-sensitivity with respect to a vector for a non-autonomous discrete system. We prove that for a periodic non-autonomous system on the closed unit interval, sensitivity is equivalent to strong…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
We unveil instances where nonautonomous linear systems manifest distinct nonuniform $\mu$-dichotomy spectra despite admitting nonuniform $(\mu, \varepsilon)$-kinematic similarity. Exploring the theoretical foundations of this lack of…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…