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The Lyapunov time mirrors the limits of the predictability of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of e. However, measures in terms of 2-foldings and 10-foldings are sometimes found, since they correspond to the loss of one bit of information or ...
There are no inherent limitations on the number of variables, parameters etc. Lyap which includes source code written in Fortran, can also calculate the Lyapunov direction vectors and can characterize the singularity of the attractor, which is the main reason for difficulties in calculating the more negative exponents from time series data.
Linear Time Invariant (LTI) Systems are those systems in which the parameters , , and are invariant with respect to time. One can observe if the LTI system is or is not controllable simply by looking at the pair ( A , B ) {\displaystyle ({\boldsymbol {A}},{\boldsymbol {B}})} .
In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is
Lyapunov fractal, bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population periodically switches between two values; Lyapunov time, characteristic timescale on which a dynamical system is chaotic; Probability theory, the branch of mathematics concerned with probability
The Golden State Warriors lost their NBA Cup game against the Denver Nuggets 119-115 on Tuesday night, and head coach Steve Kerr was not happy with the way it ended.
The concept of finite-time Lyapunov dimension and related definition of the Lyapunov dimension, developed in the works by N. Kuznetsov, [4] [5] is convenient for the numerical experiments where only finite time can be observed. Consider an analog of the Kaplan–Yorke formula for the finite-time Lyapunov exponents:
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