Conditions and regimes of population stable coexistence which are present in a discrete mathematical model host and parasite that describes interaction of two insect species are studied by analytical tools. It is shown the model possesses of two kind stable regimes at least. Species population numbers of the first one are always equal to certain constants for all times and those of the second one vary with during time chaotically, i.e. complete unpredictable manner. Parameter value domains such that a future asymptotical stable regime of population coexistence depends essentially on not only parameter values but else on initial numbers of both population are found too.