Dimensional reduction in classical Lorenz system

Abstract

Important properties of dynamical systems with a nonlocal evolution operator in the form of Caputo– Weyl are considered. A double dimensional reduction of the evolutionary operator of a special form connects various nonlinear fractional dynamical systems. For the integer values of the fractional parameter, we obtain the interrelation among various classical dynamical systems. In particular, it is shown that with a special choice of the evolution operator and dimensional reduction, the one-dimensional evolutionary Richards equation, the two-dimensional Gierer–Meinhardt system and the classical Lorenz system are closely interconnected dynamical systems.