  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. \textbf{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 $<F>$.
We find that $\triangle F\sim < F >^{\alpha}$ in the chaotic domain, where
$\alpha\approx 1$. In this domain, we also find that $<F > \sim M^{0.5}$, 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. \textbf{272}, 11 (1983); M. Wold, M. S.
Brotherton and Z. Shang, Mon. Not. R. Astron. Soc. \textbf{375}, 989 (2007)].
