Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior

Abstract

We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n−species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.

Keywords

• biological Lotka-Volterra cooperation networks
• fractional derivatives
• impulsive control
• Mittag-Leffler stability
• practical stability
• stability of sets