Optimal periodic orbits of chaotic systems

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August undefined, 2024

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. 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 …

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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 … 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. how many inches is in 20 yards

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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 … 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 … 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. how many inches is in 3 yards

Multipulse Orbits and Chaotic Dynamics of an Aero-Elastic FGP …

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. 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 … how many inches is in 2 yardsWebA 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 … how many inches is in 18 cm

"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, … " - Optimal periodic orbits of chaotic systems

Optimal periodic orbits of chaotic systems

WebEnter the email address you signed up with and we'll email you a reset link. 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 …

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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 … 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. …

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. 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 …

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

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

WebChaotic transition is also important in physiology and medicine. At present scientists are debating whether healthy biological systems are regular and predictable or chaotic. … howard e buttWebOct 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. howard e butt srWebThere 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. how many inches is in 1 foot howard e buttsWebWe 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 … howard eckstut obituaryWebNov 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 ... howard ecker and company llcWebThe 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. howard ecker chicago