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Stability of a three-dimensional diffusive Lotka–Volterra system of type-K with delays

A three-dimensional diffusive Lotka–Volterra system of type-K with delays is investigated. We give a stability analysis in detail for all equilibria of the system and obtain some threshold conditions for linear instability and linear asymptotic stability of each equilibrium. We develop the analytical method for stability analysis of reaction–diffusion equations with multi-delays.