Related papers: Chaos and Control in Nonlinear Bloch System

We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among…

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…

We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…

Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…

The main objective of this paper is to show that two asymptotically stable steady states which belong to an analytic path of asymptotically stable steady states can be gradually transferred one to the other by successive changes of the…

Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear…

Spin masers are a prototype nonlinear dynamic system. They undergo a bifurcation at a critical amplification factor, transiting into a limit cycle phase characterized by a Larmor precession around the external bias magnetic field, thereby…

For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical…

Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was…

We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…

We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector…

We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations…

We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

This paper proposes an approach to addresses the control challenges posed by a fault-induced uncertainty in both the dynamics and control input effectiveness of a class of hierarchical nonlinear systems in which the high-level dynamics is…

Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…

With $n$-body simulations we investigate the stability of tilted circumbinary planetary systems consisting of two nonzero mass planets. The planets are initially in circular orbits that are coplanar to each other, as would be expected if…

This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…

The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…