Optimal periodic orbits of chaotic systems

Author: hkyb

August undefined, 2024

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. 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 …

Stabilizing the unstable periodic orbits of a hybrid chaotic system ...

WebComputing 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. 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. ioptron versa 108 ed apochromatic refractor

Comment on "Optimal Periodic Orbits of Chaotic Systems"

WebApr 4, 2024 · Abstract Chaotic dynamics of an impulse Duffing-van der Pol system is studied in this paper. With the Melnikov method, the existence condition of transversal homoclinic point is obtained, and chaos threshold is presented. In addition, numerical simulations including phase portraits and time histories are carried out to verify the analytical results. … 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 … WebThe multipulse global bifurcations and chaotic dynamics of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectr ioptron versa 108mm ed apo reviews

MATHEMATICA tutorial, Part 2.3: Chaos - Brown University

An optimization approach to locating and stabilizing unstable periodic …

WebApr 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. WebAug 1, 2000 · (The study of optimal orbits is of interest in at least three contexts: controlling chaos, embedding of low-dimensional attractors of high-dimensional dynamical systems in low-dimensional measurement spaces, and bubbling bifurcations of synchronized chaotic systems.) Here we extend this previous work. ioptron strain waveWebMar 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 … ioptron user manual

"WebOct 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 … " - Optimal periodic orbits of chaotic systems

Optimal periodic orbits of chaotic systems

Constructing periodic orbits of high-dimensional chaotic systems …

WebJul 1, 2024 · As a classical technique for chaos suppression, the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits … WebOct 1, 2012 · Classical gradient-based optimal control methods as well as modern optimization algorithm Particle Swarm Optimization (PSO) are utilized to force the chaotic system to follow the desired UPOs. For better performance, gradient-based is applied in multi-intervals and the results are promising.

Did you know?

WebMar 1, 1996 · Europe PMC is an archive of life sciences journal literature. Search life-sciences literature (Over 39 million articles, preprints and more) WebAug 1, 2008 · Approximating the maximum ergodic average via periodic orbits - Volume 28 Issue 4. ... Optimal periodic orbits of chaotic systems occur at low period. Phys. Rev. E 54 (1996), 328 ... Optimal orbits of hyperbolic systems. Nonlinearity 12 (4) (1999), ...

WebNov 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 ... WebChaotic transition is also important in physiology and medicine. At present scientists are debating whether healthy biological systems are regular and predictable or chaotic. …

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 ... WebBound-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

WebA three-dimensional autonomous deterministic chaotic system having six parameters is explored within this article. The dynamical characteristics of the proposed system are investigated through eigenvalues structure, bifurcation diagrams, Kaplan–Yorke dimension, Lyapunov exponents, time response, and phase plane trajectories. For the …

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 ioptron updateWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor. Motivated by two different topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which … ioptron smartstar-g-r80 gps telescope ioptron ritchey-chretien telescopeWebWe consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(τ) for these systems is evaluated semiclassically in terms of periodic and diﬀractive orbits. It is shown for … on the rack phraseWebSep 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 … ioptron sync to targetWebJun 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 … ioptron technical supportWebSep 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. on the rack canada