Funciones de Dulac para modelosmatemáticos de la ecología

• Autores: Emmanuel Mendoza López, Osvaldo Osuna, Geiser Villavicencio Pulido
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 27, Nº. 2, 2020, págs. 367-382
• Idioma: español
• DOI: 10.15517/rmta.v27i2.34430
• Títulos paralelos:
  • Dulac’s functions for mathematicalecological models
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Excluir la existencia de oscilaciones sostenidas en modelos de la eco-logía matemática es de vital interés para conocer la dinámica poblacionalde especies interactuando. En este trabajo se construyen funciones de Du-lac para algunas generalizaciones de modelos usados comúnmente en laecología matemática. Dicho resultado excluye la existencia de órbitas pe-riódicas para algunos modelos que describen competencia intraespecíficao interespecífica, relaciones de competencia, de depredación y captura deindividuos de alguna de las especies

  • English

    o exclude the existence of sustained oscillations in mathematical ecol-ogy models is of vital interest to know the populational dynamics of inter-acting species. In this paper, Dulac functions are constructed for some gen-eralizations of models commonly used in populational ecology. This resultexcludes the existence of periodic orbits for some models that describe in-traspecific and / or interspecific competition, relationships of competition,predation and capture of individuals of any of the species.

• Referencias bibliográficas
  • [1] L. Cherkas, A. Grin A., Algebraic aspects of finding a Dulac function for polynomial autonomous systems on the plane, Differ. Equa., 37(2001),...
  • [2] J.R. Cooley, D.C. Marshall, K.B.R. Hill, A specialized fungal parasite (Massospora cicadina) hijacks the sexual signals of periodical...
  • [3] M.P. Kahl Jr., Food ecology of the Wood Stork (Mycteria Americana) in Florida, Ecological Monographs 34(1964), no. 2, 97–117. Doi: 10.2307/1948449
  • [4] J.D. Murray, Mathematical Biology - I. An Introduction, Springer-Verlag, New York, 2002. Doi: 10.1007/b98868
  • [5] O. Osuna, C. Vargas, Construction of Dulac functions for mathematical models in population biology, International Journal of Biomathematics,...
  • [6] O. Osuna, G. Villaseñor, On the Dulac functions, Qualitative Theory of Dynamical Systems 10(2011), no. 1, 43 49. Doi: 10.1007/s12346-011-0036-y
  • [7] O. Osuna, G. Villaseñor, Some properties of the Dulac functions set, E.J. of Qualitative Theory of Differential Equations 72(2011), 1–8....
  • [8] O. Osuna, G. Villavicencio, Generating Dulac functions for differential equations and biological models, Avanza 6(2016) FM-IIT, UACJ,...
  • [9] E. Saez, I. Szántó, On the construction of certain Dulac function, Trans. Automat. Control 33(1988), no. 9, 856. Doi: 10.1109/9.1315
  • [10] R. Sarkar, J. Chattopadhayay, Occurrence of planktonic blooms under environmental fluctuations and its possible control mechanism–Mathematical...
  • [11] M. Scheffer, Fish and nutrients interplay determines algal biomass: A minimal model, Oikos 62(1991), no. 3, 271–282. Doi: 10.2307/3545491
  • [12] T. Sota, S. Yamamoto, J.R. Cooley, K.B.R. Hill, C. Simon, J. Yoshimura, Independent divergence of 13- and 17-y life cycles among three...
  • [13] E. Venturino, The effects of the diseases on competing species, Mathematical Biosciences 174(2001), no. 2, 111–131. Doi: 10.1016/S0025-5564(01)00081-5