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

TL;DR

This paper constructs four limit cycles in specific three-dimensional Lotka-Volterra systems, providing a partial answer to a longstanding problem in the classification of such systems.

Contribution

It demonstrates the existence of at least four limit cycles in classes 28, 30, and 31 of Zeeman's classification, extending previous results to new classes.

Findings

Existence of four limit cycles in class 28

Existence of four limit cycles in class 30

Existence of four limit cycles in class 31

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].