Sentence examples for autonomous discrete from inspiring English sources

Proposition 3.4 Let ( X, f 1, ∞ ) be a k-periodic non-autonomous discrete system where ( X, d ) is a metric space, g = f k ∘ f k − 1 ∘ ⋯ ∘ f 1, ( X, g ) is its induced autonomous discrete system.

Putting (g_{n}=frac {sin epsilon }{epsilon ^{2}}) and a m =0, (3.16) recovers the autonomous discrete Burgers Eq. 3.12.

The hierarchy introduced in the previous section is sometimes referred to as the autonomous discrete Burgers hierarchy.

For the curves constructed from the shock wave solutions of the autonomous discrete Burgers hierarchy, the summation in (3.26) can be computed explicitly.

For example, Zhang et al. [5] have studied the dynamic behavior of the following autonomous discrete differential equation: Delta x(n)=-alpha x(n)+beta x n-tau) e^{-gamma x n-tau)}.

In [6], Altıntan investigated the stability for (3) by reducing it into the following autonomous discrete equation: x_{k+1}=F(x_{k})=x_{k}{ mathrm{e}}^{a-bx_{k}}, (4) where (x_{k}=x k)), (kinmathbb{N}).

The result is a direct consequence of Proposition 2.8 by equivalently representing the time-varying discrete-time system (2.10) as an autonomous discrete-time nonlinear system by appending another state to represent time.

Reaching motions are modeled as solutions to autonomous discrete-time nonlinear dynamical systems, so that the movements started near the data of the demonstrations follow the trained trajectories and always reach and stop at the target.

Let ( X, f 1, ∞ ) be a non-autonomous discrete system.

Kolyada and Snoha [1] gave the definition of topological entropy in non-autonomous discrete systems; Kolyada et al. [13] discussed minimality of non-autonomous discrete systems; Kempf [14] and Canovas [15] studied ω-limit sets in non-autonomous discrete systems.

Krabs [16] discussed stability in non-autonomous discrete systems; Huang et al. [17, 18] studied topological pressure and pre-image entropy of non-autonomous discrete systems.