Two limit cycles in three-dimensional Lotka-Volterra systems
نویسندگان
چکیده
منابع مشابه
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...
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It is known that a limit cycle (or periodic coexistence) can occur in a competitor–competitor–mutualist Lotka–Volterra system ẋ1 = x1(r1 − a11x1 − a12x2 + a13x3), ẋ2 = x2(r2 − a21x1 − a22x2 + a23x3), ẋ3 = x3(r3 + a31x1 + a32x2 − a33x3), where ri , ai j are positive real constants [X. Liang, J. Jiang, The dynamical behavior of type-K competitive Kolmogorov systems and its applications to 3-di...
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The following conjecture of M. L. Zeeman is proved. If three interacting species modeled by a competitive Lotka–Volterra system can each resist invasion at carrying capacity, then there can be no coexistence of the species. Indeed, two of the species are driven to extinction. It is also proved that in the other extreme, if none of the species can resist invasion from either of the others, then ...
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We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,−1, 1), (2,−1, 1) and (1,−2, 1)-resonance. To prove sufficiency, we mainly use the method of Darboux with extensions for inverse Jacobi multipliers, and the linearizability of a ...
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We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, Ok, k = 1, . . . , p, have two dimensional unstable manifolds that contain orbits connecting eachOk to the next two equilibrium pointsOk+1 andOk+2 in the chain (Op+1 = O1). We show that the union of these equilibria and ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2002
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(02)00129-3