The wandering of non-linear systems along the field of the possible development paths is one of the important characteristics of dynamic non-linear systems in synergetics. Insect populations are a complex of open biological systems with chaotic non-linear dynamics in space and time. Predicting their future development is not an easy task. Ignorance of the non-linear systems dynamics regularity is the cause of the repeated errors in predicting and, as a result, “sudden” appearances of “unexpected” and unpredictable mass reproductions of short-horned grasshoppers and locusts, winter moth, webworm beetle, sun pest and some other insect pests, the consequences of that are catastrophic for agriculture and forestry. In this article the authors analysed thoroughly the chronicles of the mass reproduction (wandering within the temporal and spatial limits of the natural habitat) of such species as short-horned grasshoppers and locusts, webworm beetle and sun pest. These pests have been known to mankind since time immemorial and they are extremely devastating.