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According to the long-memory principle appears in fractional-order dynamicalsystems, analysis of these systems is commonly more complicated than thosedescribed by nonlinear ordinary differential equations. Another difficulty isdue to the fact that some classical tools such as the Lyapunov stabilitytheorems cannot directly be applied to nonlinear fractional differentialsystems. The aim of this paper is to study the stability of a general form ofthe two-dimensional fractional-order Lotka-Volterra equation and numericallyinvestigate the domain of attraction of its stable equilibrium points. It isalso shown that the fractional-order Lotka-Volterra system can never have astable focus although the linearized system has complex conjugate modes. Someother properties of the fractional-order Lotka-Volterra equation, which are notobserved in integer-order case, are also discussed.

More Details on Analysis of Fractional-Order Lotka-Volterra Equation