An analytical approach to chaos in Lorenz-like systems. A class of dynamical equations
INFM, Dipartimento di Fisica, Università di Genova - I-16146
2 CNR-ISIAtA, c/o Università di Lecce - I-73100 Lecce, Italy
3 CNRS, Observatoire de la Côte d'Azur - B.P. 4229, 06304 Nice Cedex 4, France
Accepted: 17 July 2001
The mechanism responsible for the emergence of chaotic behavior has been singled out analytically within a class of three-dimensional dynamical systems which generalize the well-known E. N. Lorenz 1963 system. The dynamics in the phase space has been reformulated in terms of a first-exit-time problem. Chaos emerges due to discontinuous solutions of a transcendental problem ruling the time for a particle to cross a potential wall. Numerical results point toward the genericity of the mechanism.
PACS: 47.52.+j – Chaos / 05.45.Ac – Low-dimensional chaos
© EDP Sciences, 2001