Fractal Oscillations of Chirp Functions and Applications to Second-Order Linear Differential Equations
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-28
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We derive some simple sufficient conditions on the amplitude a(x), the phase φ(x), and the instantaneous frequency ω(x) such that the so-called chirp function y(x)=a(x)S(φ(x)) is fractal oscillatory near a point x=x0, where φ′(x)=ω(x) and S=S(t) is a periodic function on ℝ.
It means that y(x) oscillates near x=x0, and its graph Γ(y) is a fractal curve in ℝ2 such that its box-counting dimension equals a prescribed real number s∈[1,2) and the s-dimensional upper and lower Minkowski contents of Γ(y) are strictly positive and finite.
It numerically determines the order of concentration of oscillations of y(x) near x=x0.
Next, we give some applications of the main results to the fractal oscillations of solutions of linear differential equations which are generated by the chirp functions taken as the fundamental system of all solutions.
American Psychological Association (APA)
Pašić, Mervan& Tanaka, Satoshi. 2013. Fractal Oscillations of Chirp Functions and Applications to Second-Order Linear Differential Equations. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-503817
Modern Language Association (MLA)
Pašić, Mervan& Tanaka, Satoshi. Fractal Oscillations of Chirp Functions and Applications to Second-Order Linear Differential Equations. International Journal of Differential Equations No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-503817
American Medical Association (AMA)
Pašić, Mervan& Tanaka, Satoshi. Fractal Oscillations of Chirp Functions and Applications to Second-Order Linear Differential Equations. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-503817
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503817