Permanence in stochastic impulse systems

Determine the conditions under which analogous notions of permanence hold for stochastic impulse systems and compare those conditions with the deterministic permanence conditions for periodically pulsed population models.

Background

The paper develops sufficient conditions for permanence and robust permanence in deterministic n-species Lotka–Volterra-type systems subject to periodic multiplicative pulses. In the concluding discussion, the authors note that both population dynamics and pulse events may be stochastic in applications, particularly when disturbances are naturally driven by events such as hurricanes or floods. They leave unresolved the task of formulating appropriate stochastic analogues of permanence and determining how their conditions relate to the deterministic theory developed in the paper.