Optimal periodic orbits of chaotic systems

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August undefined, 2024

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. Weband such that the optimal orbit is less unstable, or even stabilized, for k>0. Periodic orbits for the controlled system can be more easily converged with traditional methods and numerical continuation in kallows one to recover optimal UPOs for the original system. The e ectiveness of this approach is illustrated on three low-dimensional ODE

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Webneighborhood of a hyperbolic point: (a) “optimal partition” of the attractor, and (b) construction of a basis set for the stationary distribution of a noisy chaotic ﬂow. B. An optimal partition from periodic orbits While in the idealized deterministic dynamics the state space can be resolved arbitrarily ﬁnely, in physical systems smart braclet with projector

Neighborhoods of periodic orbits and the stationary …

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 1, 2015 · In this paper, we are interested in the control of a chaotic hybrid system with an application to Chua’s system. It is known that chaotic attractors contain an infinite number of unstable periodic orbits (UPO) with different lengths, our idea consists in stabilizing a predetermined orbit of a given length by using an optimal control method. WebJun 27, 1997 · In a recent Letter, Hunt and Ott argued that SHORT-period unstable periodic orbits (UPOs) would be the invariant sets associated with a chaotic attractor that are most likely to optimize the time average of some smooth scalar performance function. In this Comment, we show that their conclusion does not hold generally and that optimal time … hill society harrisburg hilton

A review of periodic orbits in the circular restricted three-body ...

WebSep 1, 2000 · based on numerical experiments and analysis, it was conjectured that the optimal orbit selected from all possible orbits on a chaotic attractor is ‘‘typically’’ a … WebMar 1, 1996 · The understanding of chaotic systems can be considerably improved with the knowledge of their periodic-orbit structure. The identification of the low-order unstable … smart brain apiWebNov 20, 2011 · The stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling ... smart brain aging

"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. " - Optimal periodic orbits of chaotic systems

Optimal periodic orbits of chaotic systems

Approximating the maximum ergodic average via periodic orbits

WebAug 1, 2000 · The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in … WebIn 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, …

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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 … WebThe multipulse global bifurcations and chaotic dynamics of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectr

WebJan 15, 2024 · Birman JS Williams RF Knotted periodic orbits in dynamical systems-1 Lorenz’s equations Topology 1983 22 47 82 682059 10.1016/0040-9383(83)90045-9 0507.58038 Google Scholar; 3. Chen G Ueta T Yet another chaotic attractor Int J Bifurcation Chaos 1999 9 1465 1466 1729683 10.1142/S0218127499001024 0962.37013 Google … 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 …

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. WebJun 27, 1997 · orbits (UPOs) would be the invariant sets associated with a chaotic attractor that are most likely to optimize the time average of some smooth scalar performance …

WebThere are naturally occurring geometric spaces, called Shimura varieties, whose points classify different elliptic curves (and abelian varieties). Inside these spaces are orbits, called Hecke orbits. These orbits are not like the regular periodic orbits of the planets around the sun, but are highly unpredictable and chaotic.

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. hill sncWebSep 1, 2000 · A novel time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems. Differing from the commonly used … smart brain aging incWebEnter the email address you signed up with and we'll email you a reset link. hill son funeral home appleton cityWebBound-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 hill society harrisburgWebThere 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 ... smart bracelets for womenWebMar 25, 1996 · Optimal Periodic Orbits of Chaotic Systems Brian R. Hunt and Edward Ott Phys. Rev. Lett. 76, 2254 – Published 25 March 1996 More PDF Export Citation Abstract Invariant sets embedded in a chaotic attractor can generate time averages that differ … smart brain aiWebOct 1, 2007 · The efficiency of these algorithms for stabilization of unstable periodic orbits of the Lorenz and Rossler systems and visualization of stabilized periodic orbits are … smart brain cartoon