Title :
Reshaping Arnold tongues
Author :
Moreno-Ahedo, Luis ; Collado, Joaquín
Author_Institution :
Autom. Control Dept., CINVESTAV-IPN, Mexico City, Mexico
Abstract :
Given the Hill´s equation x¿+(¿+ßp(t)t)x=0, where ¿ and ß are parameters and p(t) is periodic. The Arnold´s tongues are the unstable regions in the ¿-ß plane where the solutions of the Hill´s equation are unbounded. We shall present some results about the reshaping of the Arnold´s tongues varying p(t) by p¿(t)=¿(p(t)+¿(t)) where the term ¿f(t) acts as control parameter. We shall present the results for the Mathieu´s equation.
Keywords :
control system synthesis; differential equations; Arnold tongues; Hill equation; Mathieu equation; control parameter; differential equation; reshaping; unstable region; Automatic control; Differential equations; Frequency; Mathematical model; Stability; Tongue;
Conference_Titel :
Electrical Engineering, Computing Science and Automatic Control,CCE,2009 6th International Conference on
Conference_Location :
Toluca
Print_ISBN :
978-1-4244-4688-9
Electronic_ISBN :
978-1-4244-4689-6
DOI :
10.1109/ICEEE.2009.5393454
