相关论文: Reducing or enhancing chaos using periodic orbits
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
In this work, we demonstrate the open-loop control of chaotic systems by means of optimized periodic signals. The use of such signals enables us to reduce control power significantly in comparison to simple harmonic perturbations. It is…
We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results…
Orbits in a three-dimensional potential subjected to periodic driving, V(x^i,t)=[1+m_0 sin(omega t) V_0(x^i), divide naturally into two types, regular and chaotic, between which transitions are seemingly impossible. The chaotic orbits…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon…
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…
We consider the break-up of invariant tori in Hamiltonian systems with two degrees of freedom with a frequency which belongs to a cubic field. We define and construct renormalization-group transformations in order to determine the threshold…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
In the present article, we introduce and also deploy a new, simple, very fast and efficient method, the Fast Norm Vector Indicator (FNVI) in order to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian…
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…
We predict theoretically and verify experimentally the suppression of chaos in the Lorenz system driven by a high-frequency periodic or stochastic parametric force. We derive the theoretical criteria for chaos suppression and verify that…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
We investigate the role of topological methods in the analysis of canard-type periodic and chaotic trajectories. In the first part of the paper, we apply topological degree to the analysis of multi-dimensional canards. The second part is…
We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…
Partial control is a technique used in systems with transient chaos. The aim of this control method is to avoid the escape of the orbits from a region Q of the phase space where the transient chaotic dynamics takes place. This technique is…
It is shown that the addition of small amounts of microscopic rods in a viscous fluid at low Reynolds number causes a significant increase of the flow resistance. Numerical simulations of the dynamics of the solution reveal that this…
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed…