Optimal periodic orbits of chaotic systems
WebMar 24, 2024 · In particular, a chaotic dynamical system is generally characterized by 1. Having a dense collection of points with periodic orbits, 2. Being sensitive to the initial condition of the system (so that initially nearby points can evolve quickly into very different states), a property sometimes known as the butterfly effect, and 3. WebThe multipulse global bifurcations and chaotic dynamics of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectr
Optimal periodic orbits of chaotic systems
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WebOptimal Periodic Orbits of Chaotic Systems Brian R. Hunt and Edward Ott Phys. Rev. Lett. 76 (1996), 2254-2257. Table of contents for this volume/issue Online abstract and download … WebFeb 22, 2012 · The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has …
WebMar 27, 2024 · A systematic method to find short unstable periodic orbits embedded in chaotic attractors is proposed. The method is based on the construction of symbolic representations of trajectories, which are used to limit the number of symbol sequences considered to find periodic orbits with a given period and also to find candidates of … WebApr 10, 2024 · Because it preserves many properties of periodic and quasiperiodic orbits of the original system and has a lower-dimensional state space, it is often used for analyzing the original system in a simpler way. In practice this is not always possible as there is no general method to construct a Poincaré map. Example 1: Forced harmonic oscillator
WebThere is a growing need for space missions that utilize orbits in the cislunar space.In the past five years,several periodic orbits in the Earth-Moon system have been utilized,such as Artimes [1] inL1/L2Lagrange points,distant retrograde orbit (DRO) of asteroid redirect mission(ARM) [2,3],Lunar Orbital Platform-Gateway (LOP-G)[4–8] in near ... WebSep 2, 2024 · Cupolets are a relatively new class of waveforms that represent highly accurate approximations to the unstable periodic orbits of chaotic systems, and large numbers can be efficiently generated via a control method where small kicks are applied along intersections with a control plane.
WebThe purpose of this paper is to mathematically establish some fundamental properties of optimal orbits: existence, sensitivity to parameter perturbations, and approximability by periodic orbits with low period. We consider only discrete-time systems (maps), and we first proveexistenceassumingonlycontinuityofthemapandtheperformancefunction.
WebHowever, chaos collapses in the digital world, specifically, chaotic systems display dynamical degradation behaviors, such as short periodic orbits, low complexity, strong correlation, uneven distribution, etc. The occurrence of these situations make the output of the chaotic system reflect these system characteristics. simpsonville christian church kyWebJul 1, 2024 · As a classical technique for chaos suppression, the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits … razor scratch on faceWebApr 14, 2024 · A framework for controlling chaotic or irregular dynamics is an effective means of obtaining regular behavior using dynamical properties. In this control scheme, unstable periodic orbits (UPOs) embedded in chaotic attractors are stabilized by small perturbations. The OGY method 22 22. E. razor scream machine drift trikeWebComputing periodic orbits for high-dimensional spatiotemporally chaotic systems remains challenging as known methods either show poor convergence properties because they are based on time-marching of a chaotic system causing exponential error amplification, or they require constructing Jacobian matrices which is prohibitively expensive. razor scraps on poston topsWebIn a closed loop, the optimal control linear system has the form of. x ... Yu, X.; Xia, Y. Detecting unstable periodic orbits in Chen’s chaotic attractor. Int. J. Bifurc. Chaos 2000, … simpsonville christian churchWebJul 1, 1996 · Optimal periodic orbits of chaotic systems occur at low period Brian R. Hunt and Edward Ott Phys. Rev. E 54, 328 – Published 1 July 1996 More PDF Export Citation Abstract Invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor. razor scraper knife in spanishWebBound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits Full Record Related Research Abstract Certain unstable periodic orbits are shown to permanently scar some quantum eigenfunctions as h..-->..0, in the sense that extra density surrounds the region of the periodic orbit. Authors: Heller, E J razor scratch on stove top