Sentence examples for reduced phase equation from inspiring English sources

In the other extreme when (alpharightarrowinfty), where the amplitude of the limit cycle decays much faster than the correlation time of the noise, then Ỹ vanishes and the reduced phase equation is simply ({mathrm {d}theta}/{mathrm {d}t}=omega+ Z(theta) xi (t)), as would be obtained using the standard phase-reduction technique without paying attention to the stochastic nature of the perturbation.

Map-reduce works in two phases: the Map phase and the reduce phase.

The Reduce stage (also called the reducing phase) aggregates values.

This stage occurs before the reduce phase.

Figure 2 The components of the reducing phase.

Substituting equation (36) into equation (3), we have the first symmetry reduced equation of equation (3) varphi_{xixixieta}+4varphi_{xixi}+4varphi_{xieta}+4varphi _{xi}varphi_{xieta}+2varphi_{xixi} varphi_{eta}+3varphi_{yy}=0.

Introduce the phase variable θ ∈ ( − π, π ] such that the dynamics of an individual limit cycle oscillator (in the absence of noise) reduces to the simple phase equation θ ˙ = ω, where ω = 2 π / T is the natural frequency of the oscillator and x ¯ ( t ) = x ∗ ( θ ( t ) ).

In the limit of weak coupling between limit-cycle oscillators, invariant manifold theory [44] and averaging theory [45] can be used to reduce the dynamics to a set of phase equations in which the relative phase between oscillators is the relevant dynamical variable.

Then, this kind of differential equation is reduced to Bessel equations and other solvable equations for six cases.

Moreover, analytical techniques can be used to reduce general oscillator models of arbitrary dimension, subject to weak inputs of a prescribed time course, down to forced scalar phase equations [24].

This equation reduces to Freundlich equation at high concentrations.