ON NUMERICAL METHODS IN LOCALIZATION PROBLEMS
- Autores: Kanatnikov A.N1,2, Tkacheva O.S1
-
Afiliações:
- Bauman Moscow State Technical University
- V.A. Trapeznikov Institute of Control Sciences of RAS
- Edição: Volume 60, Nº 11 (2024)
- Páginas: 1553-1561
- Seção: NUMERICAL METHODS
- URL: https://ter-arkhiv.ru/0374-0641/article/view/649594
- DOI: https://doi.org/10.31857/S0374064124110107
- EDN: https://elibrary.ru/JDQQEW
- ID: 649594
Citar
Resumo
When solving localization problem numerically, the main problem is to construct a universal cross section corresponding to a given localizing function. The paper proposes two methods for solving this problem, which use estimates of the first and second order derivatives. A comparative analysis of these methods with a method based on the use of all nodes of a regular grid was carried out. A comparative analysis shows that the proposed methods are superior both in terms of computational complexity and in the quality of the resulting approximation of the universal section.
Palavras-chave
Sobre autores
A. Kanatnikov
Bauman Moscow State Technical University; V.A. Trapeznikov Institute of Control Sciences of RAS
Email: skipper@bmstu.ru
Moscow, Russia
O. Tkacheva
Bauman Moscow State Technical University
Email: tkolga17@gmail.com
Moscow, Russia
Bibliografia
- Krishchenko, A.P., Localization of invariant compact sets of dynamical systems, Differ. Equat., 2005, vol. 41, no. 12, pp. 1669–1676.
- Kanatnikov, A.N. and Krishchenko, A.P., Invariantnye kompakty dinamicheskikh sistem (Invariant Compact Sets of Dynamical Systems), Moscow: Izd. MGTU im. N.E. Baumana, 2011.
- Kanatnikov, A.N. and Krishchenko, A.P., Localizing sets and trajectory behavior, Dokl. Math., 2016, vol. 94, no. 2, pp. 506–509.
- Krishchenko, A.P., Localization of simple and complex dynamics in nonlinear systems, Differ. Equat., 2015, vol. 51, no. 11, pp. 1432–1439.
- Krishchenko, A.P., Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets, Dokl. Math., 2016, vol. 94, no. 1, pp. 365–368.
- Krishchenko, A.P., Construction of Lyapunov functions by the method of localization of invariant compact sets, Differ. Equat., 2017, vol. 53, no. 11, pp. 1413–1418.
- Kanatnikov, A.N. and Krishchenko, A.P., Localization of invariant compact sets of nonautonomous systems, Differ. Equat., 2009, vol. 45, no. 1, pp. 46–52.
- Kanatnikov, A.N., Korovin, S.K., and Krishchenko, A.P., Localization of invariant compact sets of discrete systems, Dokl. Math., 2010, vol. 81, no. 2, pp. 326–328.
- Kanatnikov, A.N. and Krishchenko, A.P., Localization of compact invariant sets of continuous-time systems with disturbance, Dokl. Math., 2012, vol. 86, no. 2, pp. 720–722.
- Kanatnikov, A.N., Localization of invariant compact sets in differential inclusions, Differ. Equat., 2015, vol. 51, no. 11, pp. 1425–1431.
- Krishchenko, A.P. and Podderegin, O.A., Hopf bifurcation in a predator–prey system with infection, Differ. Equat., 2023, vol. 59, no. 11, pp. 1573–1578.
- Coria, L.N. Bounding a domain containing all compact invariant sets of the permanent-magnet motor system / L.N. Coria, K.E. Starkov // Commun. Nonlin. Sci. Numer. Simul. — 2009. — V. 14, № 11. — P. 3879-3888.
- Starkov, K.E. Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems / K.E. Starkov // Phys. Lett. A. — 2011. — V. 375, № 36. — P. 3184-3187.
- Starkov, K.E. Eradication conditions of infected cell populations in the 7-order HIV model with viral mutations and related results / K.E. Starkov, A.N. Kanatnikov // Mathematics. — 2021. — V. 9, № 16. — Art. 1862.
- Starkov, K.E. On the dynamics of immune-tumor conjugates in a four-dimensional tumor model / K.E. Starkov, A.P. Krishchenko // Mathematics. — 2024. — V. 12, № 6. — Art. 843.
- Vorkel’, A.A. and Krishchenko, A.P., Numerical analysis of asymptotic stability of equilibrium points, Mathematics Math. Model., 2017, no. 3, pp. 44–63.
Arquivos suplementares
