Related papers: Weak tracking in nonautonomous chaotic systems
We consider the monotonic tracking control problem for continuous-time single-input single-output linear systems using output-feedback linear controllers in this paper. We provide the necessary and sufficient conditions for this problem to…
There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant…
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…
Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map…
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak…
This paper considers the tracking control problem for an unknown nonlinear system with time-varying bounded disturbance subjected to a prescribed performance and input constraints. When performance and input constraints are specified…
This article discusses the weak pullback attractors for a damped stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$ with $n\geq 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a…
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…
We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Henon map. Such dynamics consists in an exponential decay of the radial component and in a…
Chaotic systems can be synchronized by linking them to a common signal, subject to certain conditions. However, the presence of multiple driving signals coming from different systems, give rise to novel behavior. The particular case of…
We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit coupled superconductors. For this purpose we formulate the bosonic field theory for fluctuations of…
In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some…
In this paper the dynamics of a fractional order system modelling the interaction between dark matter and dark energy is analytically and numerically studied. It is shown for the first time that systems modelling the interaction between…
We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
In this paper, the tracking control problem of a class of uncertain Euler-Lagrange systems subjected to unknown input delay and bounded disturbances is addressed. To this front, a novel delay dependent control law, referred as Adaptive…
Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise…
When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from…