Persons: Kulikov, Anatolii Nikolaevich

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Kulikov, Anatolii Nikolaevich

Statistics Math-Net.Ru
Total publications:	44
Scientific articles:	42
Presentations:	2

Number of views:
This page:	1086
Abstract pages:	9312
Full texts:	3808
References:	1512

Associate professor

Doctor of physico-mathematical sciences (2018)

Speciality:

01.01.02 (Differential equations, dynamical systems, and optimal control)

E-mail:

Keywords:

nonlinear panel flutter, abstract evolutionary equations, stability, bifurcations, normal forms, hard excitation of vibrations.

UDC:

517.917, 517.9, 519.624.2, 517.956.4

MSC:

34A30, 34D08, 34L40, 90C25, 65J05, 37H20

Subject:

theory of dynamical systems with infinite-dimensional phase space, invariant manifolds, normal forms, bifurcations

Main publications:

V. S. Kolesov, Yu. S. Kolesov, A. N. Kulikov, I. I. Fedik, “Ob odnoi matematicheskoi zadache teorii uprugoi ustoichivosti”, Prikladnaya matematika i mekhanika, 42:3 (1978), 458–465

https://www.mathnet.ru/eng/person18266

List of publications on Google Scholar

List of publications on ZentralBlatt

https://mathscinet.ams.org/mathscinet/MRAuthorID/216940

	Publications in Math-Net.Ru	Citations
	2024
1.	A. N. Kulikov, “On the uniqueness problem for a central invariant manifold”, TMF, 220:1 (2024), 59–73 ; Theoret. and Math. Phys., 220:1 (2024), 1110–1121
	2023
2.	A. N. Kulikov, D. A. Kulikov, “The influence of delay and spatial factors on the dynamics of solutions in the mathematical model “supply-demand””, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 230 (2023), 75–87
3.	A. N. Kulikov, D. A. Kulikov, D. G. Frolov, “The influence of competition on the dynamics of macroeconomic systems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 228 (2023), 20–31
4.	A. N. Kulikov, D. A. Kulikov, “Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto–Sivashinsky equation with allowance for dispersion”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 226 (2023), 69–79
5.	A. N. Kulikov, D. A. Kulikov, “Local attractors of one of the original versions of the Kuramoto–Sivashinsky equation”, TMF, 215:3 (2023), 339–359 ; Theoret. and Math. Phys., 215:3 (2023), 751–768
	2022
6.	A. N. Kulikov, “Invariant tori of the weakly dissipative version of the Ginzburg—Landau equation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 216 (2022), 66–75
7.	A. N. Kulikov, D. A. Kulikov, D. G. Frolov, “The Keynes model of the business cycle and the problem of diffusion instability”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 207 (2022), 77–90
8.	A. N. Kulikov, D. A. Kulikov, “Local bifurcations and a global attractor for two versions of the weakly dissipative Ginzburg–Landau equation”, TMF, 212:1 (2022), 40–61 ; Theoret. and Math. Phys., 212:1 (2022), 925–943	2
9.	A. N. Kulikov, D. A. Kulikov, “Invariant manifolds and the global attractor of the generalised nonlocal Ginzburg-Landau equation in the case of homogeneous dirichlet boundary conditions”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 38:1 (2022), 9–27
	2021
10.	A. N. Kulikov, D. A. Kulikov, “Invariant manifolds of a weakly dissipative version of the nonlocal Ginzburg–Landau equation”, Avtomat. i Telemekh., 2021, no. 2, 94–110 ; Autom. Remote Control, 82:2 (2021), 264–277	7
11.	A. N. Kulikov, D. A. Kulikov, “On the possibility of implementing the Landau–Hopf scenario of transition to turbulence in the generalized model “multiplier-accelerator””, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 203 (2021), 39–49
12.	A. N. Kulikov, D. A. Kulikov, “Attractor of the generalized Cahn–Hilliard equation, on which all solutions are unstable”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 195 (2021), 57–67
13.	A. N. Kulikov, D. A. Kulikov, “Cahn–Hilliard equation with two spatial variables. Pattern formation”, TMF, 207:3 (2021), 438–457 ; Theoret. and Math. Phys., 207:3 (2021), 782–798	3
	2020
14.	A. N. Kulikov, “Inertial invariant manifolds of a nonlinear semigroup of operators in a Hilbert space”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 186 (2020), 57–66	6
15.	A. N. Kulikov, D. A. Kulikov, “A possibility of realizing the Landau–Hopf scenario in the problem of tube oscillations under the action of a fluid flow”, TMF, 203:1 (2020), 78–90 ; Theoret. and Math. Phys., 203:1 (2020), 501–511	5
16.	A. N. Kulikov, D. A. Kulikov, “One-phase and two-phase solutions of the focusing nonlinear Schrodinger equation”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2020, no. 2, 18–34
	2019
17.	A. N. Kulikov, “Bifurcations of invariant tori in second-order quasilinear evolution equations in Hilbert spaces and scenarios of transition to turbulence”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 168 (2019), 45–52
18.	A. N. Kulikov, D. A. Kulikov, “Local bifurcations in the Cahn–Hilliard and Kuramoto–Sivashinsky equations and in their generalizations”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 670–683 ; Comput. Math. Math. Phys., 59:4 (2019), 630–643	15
	2018
19.	A. N. Kulikov, A. V. Sekatskaya, “Local Attractors in One Boundary-Value Problem for the Kuramoto–Sivashinsky Equation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148 (2018), 58–65 ; J. Math. Sci. (N. Y.), 248:4 (2020), 430–437	1
20.	A. N. Kulikov, D. A. Kulikov, “The Kuramoto–Sivashinsky equation. A local attractor filled with unstable periodic solutions”, Model. Anal. Inform. Sist., 25:1 (2018), 92–101	6
	2017
21.	A. N. Kulikov, D. A. Kulikov, “Local bifurcations in the periodic boundary value problem for the generalized Kuramoto–Sivashinsky equation”, Avtomat. i Telemekh., 2017, no. 11, 20–33 ; Autom. Remote Control, 78:11 (2017), 1955–1966	11
	2016
22.	A. N. Kulikov, D. A. Kulikov, “Nonlocal model for the formation of ripple topography induced by ion bombardment. Nonhomogeneous nanostructures”, Matem. Mod., 28:3 (2016), 33–50	7
	2015
23.	A. M. Kovaleva, A. N. Kulikov, D. A. Kulikov, “Stability and bifurcations of undulate solutions for one functional-differential equation”, Izv. IMI UdGU, 2015, no. 2(46), 60–68	2
	2012
24.	A. N. Kulikov, D. A. Kulikov, “Formation of wavy nanostructures on the surface of flat substrates by ion bombardment”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 930–945 ; Comput. Math. Math. Phys., 52:4 (2012), 800–814	31
	2011
25.	A. N. Kulikov, G. V. Pilipenko, “Resonances in the problem of the panel flutter in a supersonic gas flow”, Model. Anal. Inform. Sist., 18:1 (2011), 56–67
26.	A. N. Kulikov, D. A. Kulikov, A. S. Rudyi, “Bifurcation of the nanostructures induced by ion bombardment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 86–99	8
27.	A. N. Kulikov, “1 : 3 Resonance is a possible cause of nonlinear panel flutter”, Zh. Vychisl. Mat. Mat. Fiz., 51:7 (2011), 1266–1279 ; Comput. Math. Math. Phys., 51:7 (2011), 1181–1193	3
	2009
28.	E. S. Kokuykin, A. N. Kulikov, “Business cycles and torus in the non-homogeneous multiplier-accelerator model”, Model. Anal. Inform. Sist., 16:4 (2009), 86–95	1
29.	A. N. Kulikov, D. A. Kulikov, “After critical and precritical bifurcations of progressive wave in a generalized Ginzburg–Landau equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 4, 71–78	2
	2008
30.	E. V. Korshunova, A. N. Kulikov, “Spatial non-homogeneous invariant tori in the Multiplier-Accelerator model”, Model. Anal. Inform. Sist., 15:1 (2008), 45–50	1
31.	A. E. Kotikov, A. N. Kulikov, “Travelling waves bifurcation of the modified Ginzburg-Landau's equation”, Model. Anal. Inform. Sist., 15:1 (2008), 10–15	1
32.	A. N. Kulikov, “The attractors of two boundary value problems for a modifieded nonlinear telegraph equation”, Nelin. Dinam., 4:1 (2008), 57–68	9
33.	A. N. Kulikov, D. A. Kulikov, “Bifurcation of autowaves of generalized cubic Schrödinger equation with three independent variables”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 3, 23–34	3
	2004
34.	A. Yu. Kolesov, A. N. Kulikov, N. Kh. Rozov, “Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain”, Mat. Zametki, 75:5 (2004), 663–669 ; Math. Notes, 75:5 (2004), 617–622
	2003
35.	A. Yu. Kolesov, A. N. Kulikov, N. Kh. Rozov, “Invariant Tori of a Class of Point Transformations: Preservation of an Invariant Torus Under Perturbations”, Differ. Uravn., 39:6 (2003), 738–753 ; Differ. Equ., 39:6 (2003), 775–790	25
36.	A. Yu. Kolesov, A. N. Kulikov, N. Kh. Rozov, “Invariant Tori of a Class of Point Mappings: The Annulus Principle”, Differ. Uravn., 39:5 (2003), 584–601 ; Differ. Equ., 39:5 (2003), 614–631	21
	2001
37.	A. N. Kulikov, “Attractors of a Nonlinear Boundary Value Problem Arising in Aeroelasticity”, Differ. Uravn., 37:3 (2001), 397–401 ; Differ. Equ., 37:3 (2001), 425–429	2
	1999
38.	Yu. S. Kolesov, A. N. Kulikov, “Bifurcation of auto-oscillations in the classical system of telegraph equations with a nonclassical nonlinear boundary condition”, Mat. Zametki, 66:6 (1999), 948–951 ; Math. Notes, 66:6 (1999), 784–787	1
	1993
39.	A. N. Kulikov, “An analogue of the Hopf bifurcation theorem in a problem on the mathematical investigation of a nonlinear panel flutter with a small damping coefficient”, Differ. Uravn., 29:5 (1993), 780–785 ; Differ. Equ., 29:5 (1993), 666–671
	1992
40.	A. N. Kulikov, “Nonlinear flutter panel: the risk of hard excitation of vibrations”, Differ. Uravn., 28:6 (1992), 1080–1082	2
	1990
41.	A. N. Kulikov, V. R. Fazylov, “Convex optimization with prescribed accuracy”, Zh. Vychisl. Mat. Mat. Fiz., 30:5 (1990), 663–671 ; U.S.S.R. Comput. Math. Math. Phys., 30:3 (1990), 16–22	4
	1984
42.	A. N. Kulikov, V. R. Fazylov, “A finite method for solving systems of convex inequalities”, Izv. Vyssh. Uchebn. Zaved. Mat., 1984, no. 11, 59–63 ; Soviet Math. (Iz. VUZ), 28:11 (1984), 75–80	2

	2021
43.	V. V. Abramov, D. I. Boyarkin, I. M. Burkin, K. V. Bukhensky, O. V. Druzhinina, D. K. Egorova, R. V. Zhalnin, I. V. Ionova, A. N. Konenkov, A. N. Kulikov, A. G. Kushner, E. Yu. Liskina, S. S. Mamonov, O. N. Masina, A. K. Murtazov, A. Yu. Pavlov, P. M. Simonov, A. O. Harlamova, T. Ph. Mamedova, S. M. Muryumin, V. I. Safonkin, G. A. Smolkin, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “In memory of Terekhin Mihail Tihonovich”, Zhurnal SVMO, 23:1 (2021), 110–111
	2019
44.	V. V. Abramov, D. I. Boyarkin, I. M. Burkin, K. V. Bukhensky, O. V. Druzhinina, D. K. Egorova, R. V. Zhalnin, I. V. Ionova, A. N. Konenkov, A. N. Kulikov, A. G. Kushner, E. Yu. Liskina, S. S. Mamonov, O. N. Masina, A. K. Murtazov, A. Yu. Pavlov, P. M. Simonov, A. O. Kharlamova, T. Ph. Mamedova, S. M. Muryumin, V. I. Safonkin, G. A. Smolkin, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “To the eighty-fifth anniversary of Mikhail Tikhonovich Terekhin”, Zhurnal SVMO, 21:1 (2019), 114–115

Presentations in Math-Net.Ru

1.	Local attractors of the Cahn-Hilliard-Oono equation A. N. Kulikov, D. A. Kulikov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 8, 2023 13:10
2.	Local bifurcations in the periodic boundary value problem for the Kuramoto-Sivashinsky equation A. N. Kulikov, D. A. Kulikov International Conference on Differential Equations and Dynamical Systems July 8, 2014 16:10

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P.G. Demidov Yaroslavl State University

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