Auto-oscillation of a generalized Gause type model with a convex contraint
Authors
G. A. Degla
- Institut of Mathematics and Physical Sciences (IMSP), University of Abomey Calavi, BP 613 Porto-Novo, Benin Republic.
S. J. Degbo
- Institut of Mathematics and Physical Sciences (IMSP), University of Abomey Calavi, BP 613 Porto-Novo, Benin Republic.
M. Dossou-Yovo
- Institut of Mathematics and Physical Sciences (IMSP), University of Abomey Calavi, BP 613 Porto-Novo, Benin Republic.
Abstract
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.
Share and Cite
ISRP Style
G. A. Degla, S. J. Degbo, M. Dossou-Yovo, Auto-oscillation of a generalized Gause type model with a convex contraint, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 60--78
AMA Style
Degla G. A., Degbo S. J., Dossou-Yovo M., Auto-oscillation of a generalized Gause type model with a convex contraint. J. Nonlinear Sci. Appl. (2023); 16(1):60--78
Chicago/Turabian Style
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 Applications, 16, no. 1 (2023): 60--78
Keywords
- Generalized Gause model
- nonmonotonic numerical responses
- nonconstant death rate
- convex constraint
- global stability
- limit cycle
- Hopf bifurcation
- first Lyapunov number
MSC
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