Optimal periodic orbits of chaotic systems

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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 …

(PDF) Periodic orbits in evolutionary game dynamics: An …

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 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 … portmeirion napkin holder

Optimal periodic orbits of continuous time chaotic systems

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

A fast method to find periodic orbits in chaotic attractors with ...

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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 … 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 … options naked putWebJun 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 … portmeirion napkin rings

"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 … " - Optimal periodic orbits of chaotic systems

Optimal periodic orbits of chaotic systems

Optimal periodic orbits of continuous time chaotic systems

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. 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 …

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WebMar 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 … 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.

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 … 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 periodic orbit of low...

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. 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.

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 ...

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. options mutual fundsWebJul 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. portmeirion mug in a tinWebMar 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 … options naturopathic clinic cleveland heightsWebMar 1, 1996 · Europe PMC is an archive of life sciences journal literature. Search life-sciences literature (Over 39 million articles, preprints and more) options ndim 2WebBound-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 portmeirion nearest train stationWebMar 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. portmeirion nhs discountWeband 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 options naples fl thrift store