Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
نویسندگان
چکیده
منابع مشابه
Hamiltonian Dynamics of the Lotka-Volterra Equations
as a model for the competition of n biological species. In this model, xj represents the number of individuals of species j (so Volterra assumes xj > 0), the ajk’s are the interaction coefficients, the εj ’s and the βj’s(> 0) are parameters that depend on the environment. For example, εj > 0 means that species j is able to increase with food from the environment, while εj < 0 means that it cann...
متن کاملMultiple 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...
متن کاملLocal integrability and linearizability of three-dimensional Lotka-Volterra systems
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 ...
متن کاملThree-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 ...
متن کاملPeriodic Lotka-Volterra competition equations.
The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two o...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 1996
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/9/4/004