Geodesic
Description of Trajectories of an Evolution Operator Generated by Mosquito Population
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 2, pp. 197-207.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study discrete-time dynamical systems generated by the evolution operator of mosquito population. An invariant set is found and a Lyapunov function with respect to the operator is constructed in this set. Using the Lyapunov function, the global attraction of a fixed point is proved. Moreover, we give some biological interpretations of our results.
Keywords: Lyapunov function, fixed point, limit point
Mots-clés : invariant set 
@article{ND_2024_20_2_a0,
     author = {Z. S. Boxonov},
     title = {Description of {Trajectories} of an {Evolution} {Operator} {Generated} by {Mosquito} {Population}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {197--207},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2024_20_2_a0/}
}
TY  - JOUR
AU  - Z. S. Boxonov
TI  - Description of Trajectories of an Evolution Operator Generated by Mosquito Population
JO  - Russian journal of nonlinear dynamics
PY  - 2024
SP  - 197
EP  - 207
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2024_20_2_a0/
LA  - en
ID  - ND_2024_20_2_a0
ER  - 
%0 Journal Article
%A Z. S. Boxonov
%T Description of Trajectories of an Evolution Operator Generated by Mosquito Population
%J Russian journal of nonlinear dynamics
%D 2024
%P 197-207
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2024_20_2_a0/
%G en
%F ND_2024_20_2_a0
Z. S. Boxonov. Description of Trajectories of an Evolution Operator Generated by Mosquito Population. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 2, pp. 197-207. http://geodesic.mathdoc.fr/item/ND_2024_20_2_a0/

[1] Lyubich, Yu. I., Mathematical Structures in Population Genetics, Biomathematics, 22, Springer, Berlin, 1992, x, 373 pp. | MR | Zbl

[2] Wang, Y. and Jiang, J., “The General Properties of Discrete-Time Competitive Dynamical Systems”, J. Differential Equations, 176:2 (2001), 470–493 | DOI | MR | Zbl

[3] Devaney, R. L., An Introduction to Chaotic Dynamical Systems, 3rd ed., CRC, Boca Raton, Fla., 2022, xiii, 419 pp. | MR | Zbl

[4] Li, J., “Malaria Model with Stage-Structured Mosquitoes”, Math. Biosci. Eng., 8:3 (2011), 753–768 | DOI | MR | Zbl

[5] Li, J., Cai, L., and Li, Y., “Stage-Structured Wild and Sterile Mosquito Population Models and Their Dynamics”, J. Biol. Dyn., 11:suppl. 1 (2017), 79–101 | MR | Zbl

[6] Bilgin, A., Brett, A., Kulenović, M. R. S., and Pilav, E., “Global Dynamics of a Cooperative Discrete System in the Plane”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 28:7 (2018), 1830022, 17 pp. | DOI | MR | Zbl

[7] Rozikov, U. A. and Velasco, M. V., “A Discrete-Time Dynamical System and an Evolution Algebra of Mosquito Population”, J. Math. Biol., 78:4 (2019), 1225–1244 | DOI | MR | Zbl

[8] Rozikov, U. A., Population Dynamics-Algebraic and Probabilistic Approach, World Sci., Hackensack, N.J., 2020, xiv, 443 pp. | MR

[9] Boxonov, Z. S. and Rozikov, U. A., “A Discrete-Time Dynamical System of Stage-Structured Wild and Sterile Mosquito Population”, Nonlinear Stud., 28:2 (2021), 413–425 | MR

[10] Boxonov, Z. S. and Rozikov, U. A., “Dynamical System of a Mosquito Population with Distinct Birth-Death Rates”, J. Appl. Nonlinear Dyn., 10:4 (2021), 791–800 | DOI | MR | Zbl

[11] Boxonov, Z. S., “A Discrete-Time Dynamical System of Mosquito Population”, J. Differ. Equ. Appl., 29:1 (2023), 67–83 | DOI | MR | Zbl

[12] Mosquito Life Cycle, MosquitoControl/MosquitoLifeCycle