Optimal periodic orbits of chaotic systems
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), ... 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.
Optimal periodic orbits of chaotic systems
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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. 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, …
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 … 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.
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. 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 …
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 …
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 … danish refugee council uganda contactsWebOct 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. danish remington rolling block for saleWebJan 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 … birthday cheesecake near meWebMar 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. birthday cheers picWebMar 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 … danish refugee council uganda officesWebJun 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 … danish remodelingWebneighborhood 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 danish refugee council uganda location