Lotka-Volterra's model and migrations: Breaking of the well-known center

Mathematical and Computer Modelling

Volumn 27, Issue 4, 1998, Pages 51-61

  Poggiale, J C ^a  

^a STATION MARINE D ENDOUME   (France)

Author keywords

Bifurcation; Center manifold; Migrations; Perturbations; Predator prey models

Indexed keywords

EID: 0032006732     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(98)00005-3     Document Type: Article

References (7)

1. 1. P.M. Auger and R. Roussarie, Complex ecological models with simple dynamics: From individuals to population, Acta Biotheoretica 42, 111-136 (1994).
2. 2. J.C. Poggiale, P.M. Auger and R. Roussarie, Perturbations of Lotka-Volterra's system by behavioral sequences, Acta Biotheoretica 43, 27-39 (1995).
3. 3. S. Chow, C. Lie and D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge Press University, (1994).
4. 4. N. Fenichel, Persistance and smoothness of invariant manifolds for flows, Indiana Univ. Math. Journal 21, 193-226 (1971).
5. 5. J.E. Mardsen and M. McCracken, Hopf bifurcation and its applications, In Applied Mathematical Sciences, p. 19, Springer-Verlag, New York, (1976).
6. 6. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, (1983).
7. 7. J.C. Poggiale, Application des variétés invariantes à la modélisation de l'hétérogénéité en dynamique des populations, Ph.D. Thesis, (1994).