Stochastic Kolmogorov-type system with infinite delay

摘要

The paper considers a stochastic functional Kolmogorov-type population system with infinite delay under the general probability measures. Main aim is to show that the environment noise will not only suppress a potential population explosion but also make the solution be stochastically ultimately bounded and asymptotic stable. Moreover, two stochastic functional Lotka–Volterra equations as examples are provided to illustrate the main results.