Geodesic
A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution
Karim Amin1, 2 ; Irina Badralexi1 ; Andrei Halanay1 ; Ragheb Mghames1, 2
1 Department of Mathematics and Informatics, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania.
2 School of Arts and Sciences, Department of Mathematics and Physics, Lebanese International University, Bekaa, Lebanon.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 36.

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In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment considering the action of the immune system is presented.
DOI : 10.1051/mmnp/2021021

Karim Amin 1, 2 ; Irina Badralexi 1 ; Andrei Halanay 1 ; Ragheb Mghames 1, 2

1 Department of Mathematics and Informatics, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania.
2 School of Arts and Sciences, Department of Mathematics and Physics, Lebanese International University, Bekaa, Lebanon. 
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Karim Amin; Irina Badralexi; Andrei Halanay; Ragheb Mghames. A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 36. doi : 10.1051/mmnp/2021021. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2021021/

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