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Define the synchronization error.
Step 1. Define the synchronization error as e_{1}(t)=x t -hat{x}(t). (10).
Define the synchronization error as e ( t ) = ( x ( t ) − y ( t ) ) ∈ R n. Subtracting the drive system (1) from the response system (4) yields the dynamical system d e d t = ( A + Δ A ) e ( t ) + ( B + Δ B ) e ( t − τ ( t ) ) + f ( x ) − f ( y ) − C sat ( u ) − w ( t ).
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For larger number of elements, N, the approaches proposed in [10] remain valid whenever the coordinate transformation Xkl∥ = xk+xl (which defines the synchronization manifold) and Xkl⊥ = xk−xl (which defines the transversal manifold) successfully separates the two systems k and l from the whole network.
Let us now define the asymptotic expectation of pairwise synchronization error as (13).
We now define the asymptotic mean square time synchronization error as (15).
To discuss exponential synchronization, we define the set s ( t ) = ∑ j = 1 N ξ j x j ( t ), (2).
Coordination may be defined as the synchronization of the pay policies of distinct bargaining units.
Let us now define the asymptotic expectation of pair-wise synchronization error as (41).
(39) Therefore, for chaos synchronization, we need to define the controller U and a parameter approximation law to set the error system to converge to zero exponentially.
Although similar in modality, these terms share the same shortcomings: they describe how a mode is intended to inflate the lung, rather than defining the characteristics of synchronization or the way spontaneous breathing efforts are supported.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com