Historical behavior for a class of Lotka–Volterra systems.

It is well‐known that discrete‐time Kolmogorov systems play important role in studying predator‐prey models with interactions. A topic of this paper deals with stochastic discrete‐time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge. [ABSTRACT FROM AUTHOR]