On some features of diffusion logistics models
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 101-106
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We note that in some cases diffusion terms in an ordinary differential equations (for example, the logistic equation) can improve (weaken) sufficient conditions for the stability of a stationary solution. Examples are given.
Mots-clés : diffusion model
Keywords: stationary state, stability.
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M. V. Polovinkina. On some features of diffusion logistics models. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 101-106. http://geodesic.mathdoc.fr/item/INTO_2022_207_a10/

[1] Voropaeva O. F., Tsgoev Ch. A., “Chislennaya model dinamiki faktorov vospaleniya v yadre infarkta miokarda”, Sib. zh. industr. mat., 22:2 (2019), 13–26 | Zbl

[2] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR

[3] Zhukova I. V., Kolpak E. P., “Matematicheskie modeli zlokachestvennoi opukholi”, Vestn. SPb. un-ta. Ser. 10. Prikl. mat. Inform. Protsessy upravl., 2014, no. 3 | Zbl

[4] Kabanikhin S. I., Krivorotko O. I., “Optimizatsionnye metody resheniya obratnykh zadach immunologii i epidemiologii”, Zh. vychisl. mat. mat. fiz., 60:4 (2020), 590–600 | Zbl

[5] Kolpak E. P., Gavrilova A. V., “Matematicheskaya model vozniknoveniya kulturnykh tsentrov i techenii v zhivopisi”, Mol. uchenyi., 22 (260) (2019), 1–17

[6] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[7] Meshkov V. Z., Polovinkin I. P., Semenov M. E., “Ob ustoichivosti statsionarnogo resheniya uravneniya Khotellinga”, Obozr. prikl. prom. mat., 9:1 (2002), 226–227.

[8] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976

[9] Polovinkina M. V., Polovinkin I. P., “Ob izmenenii kharaktera ustoichivosti trivialnogo resheniya pri perekhode ot modeli so sosredotochennymi parametrami k modeli s raspredelennymi parametrami”, Prikl. mat. fiz., 52:4 (2020), 255–261

[10] Samarskii A. A., Mikhailov A. P., Matematicheskoe modelirovanie: Idei. Metody. Primery, Fizmatlit, M., 2005 | MR

[11] Svirezhev Yu. M., Logofet D. O., Ustoichivost biologicheskikh soobschestv, Nauka, M., 1978 | MR

[12] Afraimovich V., Young T., Muezzinoglu M. K., Rabinovich M. I., “Nonlinear dynamics of emotion-cognition interaction: When emotion does not destroy cognition?”, Bull. Math. Biol., 73 (2011), 266–284 | DOI | MR | Zbl

[13] Aniji M., Kavitha N., Balamuralitharan S., “Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy”, Boundary-Value Probl., 2020 (2020), 80 | DOI | MR | Zbl

[14] Brauer F., Castillo-Chavez C., Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2012 | MR | Zbl

[15] D'Onofrio A., Manfredi P., “The interplay between voluntary vaccination and reduction of risky behavior: A general behavior-implicit SIR model for vaccine preventable infections”, Current Trends in Dynamical Systems in Biology and Natural Sciences, Springer Nature, Switzerland, 2020, 185–203 | DOI | MR

[16] Friedrichs K. O., Spectral Theory of Operators in Hilbert Space, Springer-Verlag, New York–Heidelberg–Berlin, 1973 | MR | Zbl

[17] Gogoleva T. N., Shchepina I. N., Polovinkina M. V., Rabeeakh S. A., “On stability of a stationary solution to the Hotelling migration equation”, J. Phys. Conf. Ser., 1203 (2019), 012041 | DOI | MR

[18] Karev G. P., “Replicator equations and the principle of minimal production of information”, Bull. Math. Biol., 72 (2010), 1124–1142 | DOI | MR | Zbl

[19] Puu T., Nonlinear Economic Dynamics, Springer-Verlag, Berlin, 1997 | MR | Zbl

[20] Rektorys K., Variational Methods in Mathematics, Science and Engineering, Springer Science Business Media, 2012 | MR

[21] Seno H., “An SIS model for the epidemic dynamics with two phases of the human day-to-day activity”, J. Math. Biol., 80 (2020), 2109–2140 | DOI | MR | Zbl

[22] Swanson K. R., Rostomily R. C., Alvord E. C., “A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle”, Br. J. Cancer., 98:1 (2008), 113–119 | DOI