PERMANENCE AND GLOBAL STABILITY IN AN IMPULSIVE LOTKA–VOLTERRA N-SPECIES COMPETITIVE SYSTEM WITH BOTH DISCRETE DELAYS AND CONTINUOUS DELAYS

Abstract

In this paper, we formulate a robust impulsive Lotka–Volterra n-species competitive system with both discrete delays and continuous delays. Our results in this paper indicate that under the appropriate linear bounded impulsive perturbations, the impulsive delay Lotka–Volterra system remains the original permanence and globally asymptotical stability of the nonimpulsive delay Lotka–Volterra system. We show that the conditions for the permanence and globally asymptotical stability of the system depend on time delays, so, we call it "profitless".