---

Journal of Applied Nonlinear Dynamics 15(1) (2026) 133--182 | DOI:10.5890/JAND.2026.03.009

Mouhamadou Dosso, Thierry Bi Boua Lagui, Bakary Koné

UFR de Mathématiques et Informatique, Université Félix Houphouët-Boigny de cocody-Abidjan, 22 BP 582 Abidjan 22, Côte d'Ivoire

Download Full Text PDF

 

Abstract

We propose a prey-predator type model with four interacting species. We carry out a mathematical analysis of the proposed model followed by a numerical analysis. We plan to examine the dynamics of different populations in an interaction where the super predator has a diverse food source. The mathematical analysis first concerns the existence, bounding and stability (local and global using the Routh-Hurwitz criterion and the Lyapunov principle) of the solutions. In addition, we look for conditions under which solutions persist or die out. Finally, numerical simulations are carried out to illustrate the theoretical results.

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions toward improving our manuscript.

References

1. [1]	Gau, R. (2024), Contamination des Inuits au mercure par la chaîne trophique des phoques, Sciences du Vivant, 50, 50-55.

2. [2]	Morato, T., Allain, V., Hoyle, S., and Nicol, S. (2009), Tuna longline fishing around west and central Pacific seamounts, Fisheries Oceanography, 18(2), 102-112.

3. [3]	Karlin, S. and McGregor, J.L. (1957), The differential equations of birth-and-death processes, and the Stieltjes moment problem, Transactions of the American Mathematical Society, 85, 489-546.

4. [4]	Sen, D., Ghorai, S., Sharma, S., and Banerjee, M. (2021), Allee effect in prey's growth reduces the dynamical complexity in prey-predator model with generalist predator, Applied Mathematical Modelling, 91, 768-790.

5. [5]	Lu, M., Huang, J., and Wang, H. (2023), An organizing center of codimension four in a predator-prey model with generalist predator: From tristability and quadristability to transients in a nonlinear environmental change, SIAM Journal on Applied Dynamical Systems, 22, 694-729.

6. [6]	Xiang, C., Huang, J., and Wang, H. (2023), Bifurcations in Holling-Tanner model with generalist predator and prey refuge, Journal of Differential Equations, 343, 495-529.

7. [7]	Lagui, T.B.B., Dosso, M., and Sitionon, G. (2024), An analysis of some models of prey-predator interaction, WSEAS Transactions on Biology and Biomedicine, 21, 1-10.

8. [8]	Aziz-Alaoui, M.A. and Daher Okiye, M. (2003), Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling type II schemes, Applied Mathematics Letters, 16(7), 1069-1075.

9. [9]	Ghorbal, K. and Sogokon, A. (2022), Characterizing positively invariant sets: Inductive and topological methods, Journal of Symbolic Computation, 113, 1-25.

10. [10]	Chen, F., Li, Z., and Huang, Y. (2007), Note on the permanence of a competitive system with infinite delay and feedback controls, Nonlinear Analysis: Real World Applications, 8, 680-687.

11. [11]	N'Doye, I. (2011), Généralisation du lemme de Gronwall-Bellman pour la stabilisation des systèmes fractionnaires, Thèse de Doctorat, Université Henri Poincaré - Nancy 1.

12. [12]	N'Guessan, A.T. (2019), Dynamique des populations et ses motivations économiques: Cas des modèles de type Kaldor modifié, Ph.D. Thesis, Université Félix Houphouët-Boigny de Cocody-Abidjan.

13. [13]	Perko, L. (1991), Differential Equations and Dynamical Systems, 3rd ed., Springer-Verlag, New York.

14. [14]	Otto, S.P. and Day, T. (1967), A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press, Princeton.

15. [15]	Fonte, C. and Delattre, C. (2010), Un critère simple de stabilité polynomiale, in Sixième Conférence Internationale Francophone d’Automatique (CIFA 2010), Nancy, France.

16. [16]	Gantmacher, F.R. (1959), The Theory of Matrices, Chelsea Publishing Company, New York, 212-250.

17. [17]	Derivière, S. and Aziz-Alaoui, M.A. (2002), Estimation d’attracteurs étranges: application à l’attracteur de Rössler, Preprint, Université du Havre, France.

18. [18]	Zhao, L., Chen, F., Song, S., and Xuan, G. (2020), The extinction of a non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls, Mathematics, 8(2), 173.

19. [19]	Maayah, B., Moussaoui, A., Bushnaq, S., and Arqub, O.A. (2022), The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach, Demonstratio Mathematica, 55, 963-977.

20. [20]	Momani, S., Maayah, B., and Arqub, O.A. (2020), The reproducing kernel algorithm for numerical solution of Van der Pol damping model in view of the Atangana-Baleanu fractional approach, Fractals, doi:10.1142/S0218348X20400101.

21. [21]	Momani, S., Arqub, O.A., and Maayah, B. (2020), Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana-Baleanu-Caputo model of the Liénard’s equation, Fractals, doi:10.1142/S0218348X20400071.

22. [22]	Chen, F.D. (2005), On a nonlinear non-autonomous predator–prey model with diffusion and distributed delay, Journal of Computational and Applied Mathematics, 180(1), 33-49.