Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system

Interaction of Neimark-Sacker and period doubling bifurcations in a vibro-impact system

In this paper we investigate the bifurcation from an invariant closed curve (a torus in continuous-time system) to two disjoint closed curves [1]. We take a mechanical vibro-impact system as a specific example in which such a bifurcation has been reported [2]. Two possible mechanisms of such a bifurcation have been proposed earlier : (a) a period doubling bifurcation followed by a Neimark-Sacke...

Period Doubling Route to Chaos

Chaos is exhibited in the diode resonator circuit due to the unrecombined charges that cross the p-n junction when the diode is in the forward bias mode. When the diode switches biases, the charges diffuse back to their original plate making the diode act as a capacitor. The larger the forward current, the greater the amount of charges that cross the junction and the longer the system will need...

Connecting Period-Doubling Cascades to Chaos

The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a parameter often reveal a complicated intermingling of period-doubling cascades and chaos. Period doubling can be studied at three levels of complexity. The fi...

A period-doubling cascade precedes chaos for planar maps.

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain ...

Amplitude calculation near a period-doubling bifurcation: An example.