Abstract
A few mathematical problems arising in the classical synchronization theory are discussed; especially those relating to complex dynamics. The roots of the theory originate in the pioneering experiments by van der Pol and van der Mark, followed by the theoretical studies by Cartwright and Littlewood. Today, we focus specifically on the problem on a periodically forced stable limit cycle emerging from a homoclinic loop to a saddle point. Its analysis allows us to single out the regions of simple and complex dynamics, as well as to yield a comprehensive description of bifurcational phenomena in the two-parameter case. Of a particular value is the global bifurcation of a saddle-node periodic orbit. For this bifurcation, we prove a number of theorems on birth and breakdown of nonsmooth invariant tori.
Original language | English |
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Pages (from-to) | 2143-2160 |
Number of pages | 18 |
Journal | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
Volume | 14 |
Issue number | 7 |
DOIs | |
State | Published - 1 Jan 2004 |
Keywords
- Homoclinic bifurcation
- Saddle-node
- Synchronization
ASJC Scopus subject areas
- Modeling and Simulation
- Engineering (miscellaneous)
- General
- Applied Mathematics