Computation of periodic orbits in three‐dimensional Lotka‐Volterra systems |
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| Authors: | Juan F Navarro Rubén Poveda |
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| Institution: | Department of Applied Mathematics, University of Alicante, Alicante, Spain |
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| Abstract: | This paper deals with an adaptation of the Poincaré‐Lindstedt method for the determination of periodic orbits in three‐dimensional nonlinear differential systems. We describe here a general symbolic algorithm to implement the method and apply it to compute periodic solutions in a three‐dimensional Lotka‐Volterra system modeling a chain food interaction. The sufficient conditions to make secular terms disappear from the approximate series solution are given in the paper. |
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| Keywords: | Lotka‐Volterra periodic orbits Poincaré ‐Lindstedt method symbolic computation |
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