Mathematics Subject Classification: 34C25, 37C60, 37C10, 92D25, 92C50.
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Artículo
Some applications of periodic orbits for competitive systems
Algunas aplicaciones de órbitas periódicas a sistemas competitivos
1Universidad Michoacana, Facultad de Ciencias Físico-Matemáticas, Morelia, México; hdiaz@umich.mx
2Universidad Michoacana, Instituto de Física y Matemáticas, Morelia, México; osvaldo@ifm.umich.mx
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.
Probamos la existencia de órbitas periódicas para sistemas dinámicos competitivos en dos dimensiones no autónomos con dependencia periódica respecto al tiempo. La prueba es una adaptación de un resultado similar para sistemas cooperativos en [ 6 ] . También damos dos aplicaciones: un modelo de población de celulas cancerosas sometidas a un tratamiento periódico de quimioterapia como se describe en [ 4 ] y [ 3 ] para el caso cooperativo, y otro modelo de poblaciones de mosquitos interactuando con mosquitos de control estériles liberados periódicamente [ 1 ] , para el caso competitivo.
Palabras clave: sistemas competitivos; órbita periódica; angiogénesis; modelado de tratamientos de cáncer; modelo de reemplazo de población; Aedes aegypti; Wolbachia.
Mathematics Subject Classification: 34C25, 37C60, 37C10, 92D25, 92C50.
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Acknowledgements
We thank the anonymous referees for some important suggestions.
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Received: October 21, 2020; Revised: April 04, 2021; Accepted: September 16, 2021