Sentence examples for mean field dynamics from inspiring English sources

This equation was derived recently for describing the mean field dynamics of boson stars.

Some exemplary numerical evaluations of the mean field dynamics from equations (9) and following for different firing thresholds θ and different pattern size inhomogeneities σ ϕ are shown in Fig. 3.

Finally, extensive numerical results are reported to demonstrate the spectral accuracy of the methods and to show very interesting and complicated phenomena in the mean field dynamics of boson stars.

10.7554/eLife.06266.025 Appendix 1 figure 1. Mean field dynamics concord with numerical simulations.

We reduce Eq. (1) to mean field dynamics of two reputation distributions.

The observed exponent of 0.5 is generally expected for dynamical systems that exhibit pitchfork bifurcation, which is intimately related to the mean field dynamics theory of an equilibrium order parameter with Z2 symmetry, such as the Ising model near a phase transition.

The stable and unstable fixed points of the mean-field dynamics are denoted by Q + and Q -.

These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis.

Later on, Gerstner in [61] built a new approach to characterize the mean-field dynamics for the spike response model, via the introduction of suitable kernels propagating the collective activity of a neural population in time.

As in the simple maximum conductance variation case, the diffusion coefficients of the ((y^{alpha}_{t})) play no role in the above mean-field dynamics and (mathbb {E}[y^{alpha}_{t}]) is given by (8).

When making the (N_{alpha})s tend to infinity, the linear structure of the above N-neuron models w.r.t. the ((y^{i}_{t})), the linear structure of the dynamics of the ((y^{i}_{t})), and the mutual independence of the Brownian motions ((B^{i,gamma}_{t})), ((W^{j,y}_{t})), lead one to mean-field dynamics.