Chaotic Dynamics of Nonideally Driven Simple Oscillators

Abstract

We discuss the new chaotic phenomena arising from the feedback coupling of the response of a nonlinear oscillator to the driving force. The dynamics is described by two coupled autonomous second order differential equations. The fourth dimension in the state space is found to be important. For example, the simple tangent bifurcation of forced oscillations is replaced by a Feigenbaum sequence followed by a crisis, which can be understood in terms of two-dimensional Henon return map. We also argue that cross over from period doubling to intermittency scaling could be found in these systems. We concentrate in this paper to the global phase space structure and suggest the detailed study on universality and scaling of the routes to chaos as an object for further investigations.