Bifurcations of a predator-prey model with non-monotonic response function

Comptes Rendus Mathematique

Volumn 341, Issue 10, 2005, Pages 601-604

  Broer, H W ^a   Naudot, Vincent ^a   Roussarie, Robert ^b   Saleh, Khairul ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27944470009     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2005.09.033     Document Type: Article

References (12)

1. J.F. Andrews A mathematical model for the continuous of microorganisms utilizing inhibitory substrates Biotechnol. Bioeng. 10 (1968) 707-723.
2. A.D. Bazykin F.S. Berezovskaya G. Denisov Y.A. Kuznetsov The influence of predator saturation effect and competition among predators on predator-prey system dynamics Ecol. Modelling 14 (1993) 39-57.
3. H.W. Broer, V. Naudot, R. Roussarie, K. Saleh, Dynamics of a predator-prey model with non-monotonic response function, Preprint, 2005.
4. F. Dumortier R. Roussarie J. Sotomayor H. Zoladek Bifurcations of Planar Vector Fields Lecture Notes in Math. vol. 1480 1991 Springer-Verlag.
5. K. Saleh, Organising centres in semi-global analysis of dynamical systems, PhD Thesis, University of Groningen, 2005.
6. Y.A. Kuznetsov Elements of Applied Bifurcations Theory 1995 Springer-Verlag.
7. A.J. Lotka Elements of Physical Biology 1925 Williams and Wilkins Baltimore, MD
8. J.W. Milnor Topology from Differential Viewpoint 1990 The University Press of Virginia.
9. J.R. Munkres Elementary Differential Topology 1963 Princeton University Press.
10. J. Palis W. de Melo Geometric Theory of Dynamical System 1982 Springer-Verlag.
11. S. Rinaldi S. Muratori Y.A. Kuznetsov Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities Bull. Math. Biol. 55 (1993) 15-35.
12. V. Volterra Variazioni e fluttuaziono del numero di individui in specie animali conviventi Mem. Accad. Lincei 2 (1926) 31-113.