Optimal periodic orbits of chaotic systems

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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. … 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 …

Bound-state eigenfunctions of classically chaotic Hamiltonian systems …

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 … 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. philips hornhautentferner

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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 … WebSep 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 … 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. philips horgen

Stabilizing unstable periodic orbits of chaotic systems via …

Constructing periodic orbits of high-dimensional chaotic systems …

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 ... 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 philips horbWebComputing 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. philips horncastle

"WebMar 1, 1996 · Europe PMC is an archive of life sciences journal literature. Search life-sciences literature (Over 39 million articles, preprints and more) " - Optimal periodic orbits of chaotic systems

Optimal periodic orbits of chaotic systems

Harmonic balance-based approach for optimal time delay …

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

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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 … 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), ...

WebCiteSeerX - 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 … WebJul 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 …

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

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, … truth pressed to the ground will rise againWebA 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 … truth press newsWebThere 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. philips horb am neckarWeband 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 truth pressWebOct 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. truthpress newsWebBound-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 philips horticultureWebJan 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 … truthpressnews network