Computation of periodic orbits in three-dimensional Lotka-Volterra systems
نویسندگان
چکیده
منابع مشابه
Three-Dimensional Competitive Lotka-Volterra Systems with no Periodic Orbits
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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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 ...
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ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2017
ISSN: 0170-4214
DOI: 10.1002/mma.4522