Lorenz-like systems and classical dynamical equations with memory forcing: an alternate point of view for singling out the origin of chaos.
An alternate view for the emergence of chaos in Lorenz-like systems is presented in this paper. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one-dimensional motion of a particle in a two-well potential, with a forcing term depending on the "memory" of the particle past motion. The dynamics of the original Lorenz system in the proposed particle phase space can then be rewritten in terms of a one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system that preserves all the essential properties of the original model.
Festa
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INFM-Department of Physics, University of Genova, I-16146 Genova, Italy.
Mazzino
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Vincenzi
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