Geodesic
Auto-oscillation of a generalized Gause type model with a convex contraint
Degla, G. A. 1 ; Degbo, S. J. 1 ; Dossou-Yovo, M. 1
1 Institut of Mathematics and Physical Sciences (IMSP), University of Abomey Calavi, BP 613 Porto-Novo, Benin Republic
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 1, p. 60-78.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we study the generalized Gause model in which the functional and numerical responses of the predators need not be monotonic functions and the intrinsic mortality rate of the predators is a variable function. As a result, we have established sufficient conditions for the existence, uniqueness and global stability of limit cycles confined in a closed convex nonempty set, by relying on a recent Lobanova and Sadovskii theorem. Moreover, we prove sufficient conditions for the existence of Hopf bifurcation. Eventually using scilab, we illustrate the validity of the results with numerical simulations.
DOI : 10.22436/jnsa.016.01.06
Classification : 92F05, 92B05, 37N25, 37G15
Keywords: Generalized Gause model, nonmonotonic numerical responses, nonconstant death rate, convex constraint, global stability, limit cycle, Hopf bifurcation, first Lyapunov number

Degla, G. A.  1 ; Degbo, S. J.  1 ; Dossou-Yovo, M.  1

1 Institut of Mathematics and Physical Sciences (IMSP), University of Abomey Calavi, BP 613 Porto-Novo, Benin Republic 
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Degla, G. A. ; Degbo, S. J. ; Dossou-Yovo, M. . Auto-oscillation of a generalized Gause type model with a convex contraint. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 1, p. 60-78. doi : 10.22436/jnsa.016.01.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.01.06/

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