Finite sequences of remerging period-doubling bifurcations have been recently observed in a variety of physically interesting dynamical systems. We show here that such remerging Feigenbaum trees are quite common in models with more than one parameter and discuss a number of criteria under which they are generally observed. These criteria are applied to simple mappings as well as the conservative Duffing's equation where the formation of a primary "bubble" is seen to lead to higher-order bubbles and hence to remerging Feigenbaum sequences. In the case of Duffing's equation, we follow the development of one such sequence, with the aid of the variation of the winding number along a symmetry axis of the problem.
ASJC Scopus subject areas
- Physics and Astronomy(all)