Related papers: Topologically Stable Equicontinuous Non-Autonomous…
We study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
In this paper, we introduce topologically stable points, $\beta$-persistent points, $\beta$-persistent property, $\beta$-persistent measures and almost $\beta$-persistent measures for first countable Hausdorff group actions of compact…
We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of…
Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for…
The stability theory of compact metric spaces with positive topological dimension is a well-established area in Dynamical Systems. A central result, attributed to Walters, connects the concepts of topological stability and the shadowing…
We analyze the stability under time evolution of complexifier coherent states (CCS) in one-dimensional mechanical systems. A system of coherent states is called stable if it evolves into another coherent state. It turns out that a system…
We propose sufficient conditions for existence of topologically stable periodic canard solutions in non-smooth slow-fast systems.
We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-balanced equilibrium (in every stoichiometric class and for…
In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system $(X,f)$ has shadowing, then it is…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis…
We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…