Abstract
This paper considers a stochastic competitive model with infinite delay and general Lévy jumps. Sufficient conditions for stability in time average are established as well as permanence in time average and extinction. The easily verifiable sufficient criteria for the existence of stability in distribution are established. Our results reveal that, firstly, stability in time average, permanence in time average and extinction have close relationships with general Lévy jumps; secondly, based on a simple assumption, infinite delays are disadvantageous to permanence in time average and stability in distribution. Finally, numerical simulations are introduced to support the theoretical analysis results.
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