Optimal periodic orbits of chaotic systems
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. 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
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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 … 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.
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 ... 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), ...
WebChaotic transition is also important in physiology and medicine. At present scientists are debating whether healthy biological systems are regular and predictable or chaotic. … 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. …
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 …
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 … order for processional weddingWebThere 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 ... order for playing cardsWebMar 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 … irds treatmentWebOct 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. order for productionWebA 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 … order for planet of the apes moviesWebThe multipulse global bifurcations and chaotic dynamics of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectr order for possession and sale of propertyWebThere 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. irdw poland