  If you are given a simple three-dimensional autonomous quadratic system that
has only one stable equilibrium, what would you predict its dynamics to be,
stable or periodic? Will it be surprising if you are shown that such a system
is actually chaotic? Although chaos theory for three-dimensional autonomous
systems has been intensively and extensively studied since the time of Lorenz
in the 1960s, and the theory has become quite mature today, it seems that no
one would anticipate a possibility of finding a three-dimensional autonomous
quadratic chaotic system with only one stable equilibrium. The discovery of the
new system, to be reported in this Letter, is indeed striking because for a
three-dimensional autonomous quadratic system with a single stable node-focus
equilibrium, one typically would anticipate non-chaotic and even asymptotically
converging behaviors. Although the new system is not of saddle-focus type,
therefore the familiar \v{S}i'lnikov homoclinic criterion is not applicable, it
is demonstrated to be chaotic in the sense of having a positive largest
Lyapunov exponent, a fractional dimension, a continuous broad frequency
spectrum, and a period-doubling route to chaos.
