A 3D competitive Lotka-Volterra equation with two limit cycles is constructed. Keywords-Lotka-Volterra equations, Competitive systems, Limit cycles, Hopf bifurcation. INTRODUCTION It is a classical result (due to Moisseev 1939 and/ or Bautin 1954, see [l, p. 213, Section 12, Example 71 or [2, 18.21) that 2D Lotka-Volterra equations cannot have limit cycles: if there is a periodic orbit, then th...

The existence of positive periodic solutions of discrete nonautonomous Lotka-Volterra systems with delays is studied by applying the continuation theorem of coincidence degree theory.

In this paper we study the global dynamics of 3–dimensional predator prey Lotka–Volterra systems, which describes two predators competing for food or shared one resource. From theoretical analysis on all parameters of this system, we show that if the resource for prey is limited, then there exist some values of parameters such that two predators and one prey coexist and their population are asy...

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters. 1. The Periodic Lotka-Volterra System. Consider the Predator-Prey model (see Volterra [1]) N ′ 1 = (ε1 − γ1N2)N1 N ′ 2 = (−ε2 + γ2N1)N2. (1) The functions N1 and N2 measure the ...