Reaction of two simple nonlinear dynamical systems to constant forcing

S. PANCHEV, T. S. SPASSOVA

Abstract

Generally, the nonlinear dynamical systems (NDSa) described by systems of nonlinear ordinary differential equations, are sensitive to structural changes of the latter. Even simple additive constants can change the global behaviour of a given system, e.g. (1.4) below. To study directly this effect we choose two popular (NDSa) - the Lorenz classical system (1.2), (1.3) and the Wiin-Nielsen system (1.6), both having various meteorological applications. Moreover, we ask and give an answer to the nonstandard problem - what should be the additive constant forcing of these systems in order to have a desired number of real fixed points with desired stability properties? Some preliminary numerical results are also presented.

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