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

Entropy (Basel). 2020 Aug 31;22(9):970. doi: 10.3390/e22090970.

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