Abstract

DIAZ-MARIN, Homero G.  and  OSUNA, Osvaldo. Some applications of periodic orbits for competitive systems. Rev. Mat [online]. 2022, vol.29, n.1, pp.53-68. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v29i1.40956.

We prove existence of periodic orbits for non-autonomous two dimensional competitive dynamical systems with periodic time dependence. The proof is an adaptation of a similar assertion stated for cooperative systems in [ 6 ]. We also give two main applications: one model for cancer cell populations under periodic chemotherapy as treated in [ 4 ] and [ 3 ] for the cooperative case, and another model for mosquito population replacement dynamics interacting with control sterile mosquitoes with periodic release [ 1 ] , for the competitive case.

Keywords : competitive systems; periodic orbit; angiogenesis; cancer treatment modeling; population replacement modeling; Aedes aegypti; Wolbachia..

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