Four limit cycles in three-dimensional Lotka-Volterra competitive systems with classes 28, 30 and 31 in Zeemans classification via automatic search

Abstract

Four limit cycles are constructed for classes 28, 30 and 31 in Zeeman's classification, together with the results in [5 ] for class 27, [20] for class 29 and [22] for class 26 which indicate that for each class among classes 26-31, there exist at least four limit cycles. This gives a partial answer to a problem proposed in [22] as well as in [7].