Related papers: Weak tracking in nonautonomous chaotic systems

In this paper, for nonautonomous dynamical systems, we give first general conditions ensuring that a pullback attractor is a forward attractor as well in both the single and multivalued frameworks. In particular, we consider asymptotically…

Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…

In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…

We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…

We study diffusion in a one-dimensional periodic array of scatterers modeled by a simple map. The chaotic scattering process for this map can be changed by a control parameter and exhibits the dynamics of a crisis in chaotic scattering. We…

This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…

We investigate how a weak constant force becomes detectable through fluctuations in anomalous transport in strongly heterogeneous media. Rather than focusing on the mean drift, we show that the key signature of the force appears in the…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. In particular, as a dissipative model we consider the spin-orbit problem…

We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a…

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution…

A chaotic autonomous Hamiltonian systems, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution - the Gibbs…

It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…

We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…

The authors investigate the impact of external sources on the pattern formation of concentration profiles of passive tracers in a two-dimensional shear flow. By using the pullback attractor technique for the associated nonautonomous…

We study Poincare recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is not supported anymore solely by unstable periodic orbits…