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A function f defined on a subset S subset R^n is said to be pseudoconcave if -f is pseudoconvex.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The system of partial differential equations E_t-v = 0 (1) r_x+omegav = 0 (2) q_x+Ev = 0 (3) v_x-omegar-Eq = 0. (4)

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

A method for predicting the onset of widespread chaos.

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

The partial differential equation del ^2u+lambda^2sinhu=0, where del ^2 is the Laplacian (Ting et al. 1987; Zwillinger 1997, p. 135).

A fixed point for which the eigenvalues are complex conjugates.

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.