Limit Cycles for the Competitive Three Dimensional Lotka–Volterra System

Multiple Limit Cycles for Three Dimensional Lotka-Volterra Equations

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...

Limit Cycles Bifurcated from a Center in a Three Dimensional System

Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the 1-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical qua...

Limit Cycles for a Class of Three Dimensional Polynomial Differential Systems

Small amplitude limit cycles for the polynomial Liénard system

We prove a quadratic in m and n estimate for the maximal number of limit cycles bifurcating from a focus for the Liénard equation  x+f(x) _ x+ g(x) = 0; where f and g are polynomials of degree m and n respectively. In the proof we use a bound for the number of double points of a rational a¢ ne curve.

Optimal accumulation of pollution: Existence of limit cycles for the social optimum and the competitive equilibrium

This paper extends the recent investigation of Tahvonen and Withagen (1996, Journal of Economic Dynamics and Control 20, 1775}1795) for costly and thus sluggish instead of instantaneous reductions in emissions. In addition to the social optimum, the paper investigates the competitive equilibrium. This plausible extension allows to derive limit cycles as the outcome for both, the social optimum ...