Related papers: An analytic system with a computable hyperbolic si…

In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with…

The aim of this paper is to show that the existence of attracting sets for quasiperiodically forced systems can be extended to appropriate skew-products on the cylinder, homotopic to the identity, in such a way that the general system will…

We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space,…

We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding basins of attraction are found to depend strongly on the full…

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that…

In this paper the attractors synthesis algorithm for a class of dissipative dynamical systems with hyperbolic equilibria, presented in [1], is applied to generate any attractor of the Rikitake system. By switching periodically, or even…

We show that a sectional-hyperbolic attracting set for a H\"older-$C^1$ vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these…

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is…

In magnetic systems with dominating easy-plane anisotropy the magnetization can be described by an effective one dimensional equation for the in-plane angle. Re-deriving this equation in the presence of spin-transfer torques, we obtain a…

Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…

The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…

We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…

In this paper, we develop a methodology for finite time rotor angle stability analysis using the theory of normal hyperbolic surfaces. The proposed method would bring new insights to the existing techniques, which are based on asymptotic…

This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…

Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…

This work contains the results from a comprehensive study of a new class of attractors. The attractors in this class are characterized by strong local instability, but they are not uniformly hyperbolic. Rigorous results on their dynamical,…

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear…