Sentences with phrase «as ordinary differential equations»

Not exact matches

Complex nonlinear multivariate systems often exhibit «strange attractors» — local fixed points in a set of coupled nonlinear ordinary differential equations — that function as foci for Poincare cycles in the multivariate phase space.

In a system such as the climate, we can never include enough variables to describe the actual system on all relevant length scales (e.g. the butterfly effect — MICROSCOPIC perturbations grow exponentially in time to drive the system to completely different states over macroscopic time) so the best that we can often do is model it as a complex nonlinear set of ordinary differential equations with stochastic noise terms — a generalized Langevin equation or generalized Master equation, as it were — and average behaviors over what one hopes is a spanning set of butterfly - wing perturbations to assess whether or not the resulting system trajectories fill the available phase space uniformly or perhaps are restricted or constrained in some way.