  According to the long-memory principle appears in fractional-order dynamical
systems, analysis of these systems is commonly more complicated than those
described by nonlinear ordinary differential equations. Another difficulty is
due to the fact that some classical tools such as the Lyapunov stability
theorems cannot directly be applied to nonlinear fractional differential
systems. The aim of this paper is to study the stability of a general form of
the two-dimensional fractional-order Lotka-Volterra equation and numerically
investigate the domain of attraction of its stable equilibrium points. It is
also shown that the fractional-order Lotka-Volterra system can never have a
stable focus although the linearized system has complex conjugate modes. Some
other properties of the fractional-order Lotka-Volterra equation, which are not
observed in integer-order case, are also discussed.
