The eccentric luminosity variation of quasars is still a mystery .
Analytic results of this behavior ranged from multi-periodic behavior to a purely random process .
Recently , we have used nonlinear time-series analysis to analyze the light curve of 3C 273 and found its eccentric behavior may be chaos [ L. Liu , Chin. J. Astron. Astrophys . 6 , 663 ( 2006 ) ] .
This result induces us to look for some nonlinear mechanism to explain the eccentric luminosity variation .
In this paper , we propose a simple non-linear accretion disk model and find it shows a kind of chaotic behavior under some circumstances .
Then we compute the outburst energy \triangle F , defined as the difference of the maximum luminosity and the minimum luminosity , and the mean luminosity \langle F \rangle .
We find that \triangle F \sim \langle F \rangle ^ { \alpha } in the chaotic domain , where \alpha \approx 1 .
In this domain , we also find that \langle F \rangle \sim M ^ { 0.5 } , where M is the mass of central black hole .
These results are confirmed by or compatible with some results from the observational data analysis [ A. J. Pica and A. G. Smith , Astrophys. J . 272 , 11 ( 1983 ) ; M. Wold , M. S. Brotherton and Z. Shang , Mon. Not. R. Astron. Soc . 375 , 989 ( 2007 ) ] .