The Lorenz chaotic systems as nonlinear oscillators with memory
Main Article Content
Abstract
Nonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generating chaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract useful information. In this paper the original Lorenz system and its modifications are reduced to single oscillatory type integral-differential equations with delayed argument. This yields to appearance of an ‘‘endogenous’’ term interpreted as memory for the past. Moreover, the equations are valid far from the initial instant (theoretically at t→∞), when the system eventually evolves on its attractor set. This corresponds to the numerical solutions when an appropriate initial part of the iterates is usually discarded to eliminate the transients. Besides, the form of the equations allows statistical treatment.
Downloads
Download data is not yet available.
Article Details
Once an article is accepted for publication, the author(s) agree that, from that date on, the owner of the copyright of their work(s) is Atmósfera.
Reproduction of the published articles (or sections thereof) for non-commercial purposes is permitted, as long as the source is provided and acknowledged.
Authors are free to upload their published manuscripts at any non-commercial open access repository.