Automatic search for multiple limit cycles in three-dimensional Lotka–Volterra competitive systems with classes 30 and 31 in Zeeman's classification

Abstract

Among the six classes of Zeeman's classification for three-dimensional Lotka–Volterra competitive systems with limit cycles, besides the classes 26, 27, 28 and 29, multiple limit cycles are found in classes 30 and 31 by an algorithmic method proposed by Hofbauer and So [J. Hofbauer, J.W. So, Multiple limit cycles for three-dimensional Lotka–Volterra equations, Appl. Math. Lett. 7 (1994) 65–70]. This also gives an answer to a problem proposed in [J. Hofbauer, J.W. So, Multiple limit cycles for three-dimensional Lotka–Volterra equations, Appl. Math. Lett. 7 (1994) 65–70].