Contribution to Competing Species Modeling with Distributed Delay
Issue | Vol. 5 Núm. 1 (2022): Ciencia, Ambiente y Clima |
DOI | |
Publicado | jul 29, 2022 |
Estadísticas |
Resumen
In this paper a competing species model is analyzed taking into account the seminal paper of Hsu, Hubbell and Waltman (1978), where two predators compete for a common prey without interference between rivals. Here a distributed delay is introduced in each one of the equations of the predator populations in the same way as suggested by Wolkowicz, Xia & Ruan (1997), in order to model the conversion time lag of consumed prey biomass into predator biomass. Using the linear trick chain technique, the solutions are analyzed from an “equivalent system” of ordinary differential equations looking to answer under what conditions will neither, one, or both species of predator populations survive, giving the appropriate insight of the biological point of view.
Cavani, M. & Farkas, M. (1994). Bifurcations in predator-prey model with memory and diffusion. I: Andronov-Hopf bifurcation. Acta Mathematica Hungarica, 63, 213-229.
Cavani, M., Lizana, M., & Smith, H. L. (2000). Stable periodic orbits for a predator-prey model with delay. Journal of Mathematical Analysis and Applications, 249, 324-339.
Cushing, J. M. (1977). Integrodifferential Equations and Delay Models in Population Dynamics 20, Heidelberg: Springer-Verlag.
Gopalsamy, K. (1992). Stability and Oscillations in Delay Differential Equations of Populations. Dynamics The Netherlands: Kluwer, Dordrecht.
Hsu, S. B. (1978). Limiting behavior for competing species. SIAM Journal on Applied Mathematics. 34, 760-763.
Hsu, S. B., Hubbell, S. P., & Waltman, P. (1977). A mathematical theory for single-nutrient competition in continuous culture of micro-organisms. SIAM Journal on Applied Mathematics. 32, 366-383.
Hsu, S. B., Hubbell, S. P., & Waltman, P. (1978a). A contribution to the theory of Competing Predators. Ecological Monographs, 48, 337-349.
Hsu, S. B., Hubbell, S. P., & Waltman, P. (1978b). Competing Predators. SIAM Journal on Applied Mathematics. 35, 617-625.
MacDonald, N. (1978). Time Lags in Biological Models, Lecture Notes in Bio-mathematics, 27, Heidelberg: Springer-Verlag.
Markus, L. (1956). Asymptotically autonomous differential systems, Contribution to the Theory of Nonlinear Oscillations 3. New Jersey: Princeton University Press.
Miller, R. K. (1971). Nonlinear Volterra Integral Equations. W. A. Benjamin (ed.). California: Menlon Park.
Smith, H. L. (2008). Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems: An Introduction to the Theory of Competitive and Cooperative Systems. New York: American Math. Soc.
Thieme, H. R. (1993). Persistence under relaxed point-dissipativity (with application to an epidemic model). SIAM Journal on Applied Mathematics, 24, 407-435.
Wolkowicz, G., H. Xia, H., & Ruan, S. (1997). Competition in the Chemostat: A distributed delay model and its global asymptotic behavior. SIAM Journal on Applied Mathematics, 57, 1281-1310.
- Resumen visto - 176 veces
- PDF descargado - 91 veces
- HTML descargado - 10 veces
Descargas
Licencia
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
Copyright
© Science, Environment and Climate, 2022
Afiliaciones
Mario Cavani
Universidad de Oriente. Cumana, Venezuela