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 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. - Abstract

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 ... 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 curing depression with diet and exercise

Constructing periodic orbits of high-dimensional chaotic systems …

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. 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 … 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 … easy ginger sponge cake