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Fractal oscillations of chirp functions and applications to second-order linear differential equations (CROSBI ID 191272)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Pašić, Mervan ; Tanaka, Satoshi Fractal oscillations of chirp functions and applications to second-order linear differential equations // International journal of differential equations, 2013 (2013), 1-11. doi: http://www.hindawi.com/journals/ijde/2013/857410/

Podaci o odgovornosti

Pašić, Mervan ; Tanaka, Satoshi

engleski

Fractal oscillations of chirp functions and applications to second-order linear differential equations

We derive some simple sufficient conditions on the amplitude $a(x)$, the phase $\varphi (x)$ and the instantaneous frequency $\omega (x)$ such that the so-called chirp function $y(x)=a (x)\, S(\varphi (x))$ is fractal oscillatory near a point $x=x_0$, where $\varphi' (x)=\omega(x)$ and $S=S(t)$ is a periodic function on $\mathbb{;R};$. It means that $y(x)$ oscillates near $x=x_0$ and its graph $\Gamma (y)$ is a fractal curve in $\mathbb{;R};^2$ such that its box-counting dimension equals to a prescribed real number $s\in [1, 2)$ and the $s$-dimensional upper and lower Minkowski contents of $\Gamma (y)$ are strictly positive and finite. It numerically determines the order of concentration of oscillations of $y(x)$ near $x=x_0$. 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.

chirp; fractal; oscillation; box dimension; differential equations

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nije evidentirano

nije evidentirano

nije evidentirano

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Podaci o izdanju

2013

2013.

1-11

objavljeno

1687-9643

1687-9651

http://www.hindawi.com/journals/ijde/2013/857410/

Povezanost rada

Temeljne tehničke znanosti, Matematika

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