MR item for 96g:34063

Josef Hofbauer and Joseph So:
Multiple limit cycles for three-dimensional Lotka-Volterra equations.
Appl. Math. Lett. 7 (1994), no. 6, 65-70.
Three-dimensional competitive Lotka-Volterra systems are considered here with an equilibrium point in the positive octant of the phase space. It is shown that among these systems there are such that have more than one limit cycle around the equilibrium point. Actually, a system with this property is explicitly constructed. The system presented is permanent, i.e. the boundary of ${\bf R}\sp 3\sb +$ is repelling; the equilibrium has a pair of imaginary eigenvalues and it is repelling on its centre manifold. This implies the existence of at least one limit cycle around the equilibrium. Then, by varying the parameters slightly, the equilibrium undergoes an inverted subcritical Hopf bifurcation, i.e. an additional unstable limit cycle arises. Several open problems are raised in the paper. The authors conjecture that the maximum number of limit cycles in such systems is 2. However, see Zhengyi Lu and Yong Luo: Three Limit Cycles for a Three-Dimensional Lotka-Volterra Competitive System with a Heteroclinic Cycle, Computers and Mathematics with Applications 46 (2003) 231-238

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