Local atractivity in zip bifurcation
Main Article Content
Keywords
zip bifurcation, k–strategist, r–strategist, functional response, dinamical population, competitive exclusion principle.
Abstract
In this paper the local segment attractiveness equilibrium that forms on the phenomenon of zip bifurcation for a three–dimensional system of differential equations nonlinear is studied. This work may be regarded as a generalization as a result on Farkas’s zip bifurcation in competition models.
MSC: 34K18
Downloads
References
[2] S. B. Hsu, S. P. Hubbel and P. Waltman. Competing predators. SIAM Journal on Applied Mathematics, ISSN 0036–1399, 35(4), 617–625 (1978).
[3] A. Koch. Coexistence resulting from an alteration of dendity dependent and density independent growth. Journal of Theoretical Biology, ISSN 0022–5193, 44, 373–386 (1974).
[4] H. L. Smith. The interaction of steady state and Hopf bifurcations in a two predator–one–prey competition model . SIAM Journal on Applied Mathematics, ISSN 0036–1399, 42(1), 27–43 (1982).
[5] D. R. Wilken. Some remarks on a competing predators problem. SIAM Journal on Applied Mathematics, ISSN 0036–1399, 42(4), 895–902 (1982).
[6] G. J. Butler. Competitive predator–prey systems and coexistence, in Population biology proceedings (Edmonton 1982). Lecture notes in biomathematics, 52: Berlin: Springer–Verlag, 210–217 (1983).
[7] M. Farkas. Zip bifurcation in a competition model . Nonlinear analysis: Theory, Methods & Applications, ISSN 0362–546X, 8(11), 1295–1309 (1984).
[8] M. Farkas. A zip bifurcation arising in population dynamics, in 10th Int. Conf. On, nonlinear oscilations, Varna 1984. Sofia: Bugarian Academy of Science, 150–155 (1985).
[9] M. Farkas, E. Sáez and Szántó. Velcro bifurcation in competition models with generalized holling functional response. Miskolc mathematcal notes, ISSN 1787–2413, 6(2), 185–195 (2005).
[10] J. D. Ferreira and Luis A. Fernandes de Oliveira. Hopf and zip bifuration in an specfic (n + 1)–competitive system, matematics. Matemáticas: Enseñanza Universitaria, ISSN 0120–6788, XV(1), 33–50 (2007).
[11] C. Escobar. Modelo original de tipo exponencial algebraico que exhibe la bifurcación zip. Tesis de maestría, Universidad de Antioquia, 2003.
[12] M. Farkas. Competitive exclusión by zip bifurcation in ”Dynamical Systems, IIASA Workshop 1985 Sopron”. Lecture Notes in Economics and Mathematical Systems, ISSN 0075–8442, 287. Springer–Verlag, 165–178 (1987).
[13] Philip Hartman. Ordinary differential equations. John Wiley & Sons, New York, 61–63 (1964).