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The system of ordinary differential equations u^' = A+u^2v-(B+1)u (1) v^' = Bu-u^2v (2) (Hairer et al. 1987, p. 112; Zwillinger 1997, p. 136). The so-called full Brusselator ...

Harmonic coordinates satisfy the condition Gamma^lambda=g^(munu)Gamma_(munu)^lambda=0, (1) or equivalently, partial/(partialx^kappa)(sqrt(g)g^(lambdakappa))=0. (2) It is ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

Tarski's theorem says that the first-order theory of reals with +, *, =, and > allows quantifier elimination. Algorithmic quantifier elimination implies decidability assuming ...

Catastrophe theory studies how the qualitative nature of equation solutions depends on the parameters that appear in the equations. Subspecializations include bifurcation ...

A class formed by sets in R^n which have essentially the same structure, regardless of size, shape and dimension. The "essential structure" is what a set keeps when it is ...