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Computation of periodic orbits in three‐dimensional Lotka‐Volterra systems
Author(s) -
Navarro Juan F.,
Poveda Rubén
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4522
Subject(s) - mathematics , computation , nonlinear system , periodic orbits , differential equation , symbolic computation , series (stratigraphy) , mathematical analysis , algorithm , paleontology , physics , quantum mechanics , biology
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.