Publications
- Bratus, A. S., Drozhzhin, S., Korushkina, A. V., Novozhilov, A. S. (2024). Food webs and the principle of evolutionary adaptation. Physica A: Statistical Mechanics and its Applications, 633, 129416.
- Bratus, A. S., Chmereva, O. S., Yegorov, I., Novozhilov, A. S. (2023). On a hypercycle equation with infinitely many members. Journal of Mathematical Analysis and Applications, 126988.
- Bratus A.S., Novozhilov A.S., Yakushkina T. (2021) Geometry of Fitness Surfaces and Dynamics of Replicator Systems. In: Mondaini R.P. (eds) Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells. BIOMAT 2020. Springer, Cham. https://doi.org/10.1007/978-3-030-73241-7_5
- Yegorov, I., Novozhilov, A. S., Bratus, A. S. Open Quasispecies Models: Stability, Optimization, and Distributed Extension, 2020, 481(2): 123477, 28 pages
- Karev, G.P., Novozhilov, A.S.: How trait distributions evolve in populations with parametric heterogeneity, Mathematical Biosciences, 2019, 315, article 108305, https://doi.org/10.1016/j.mbs.2019.108235
- Semenov, Y.S., Novozhilov A.S.: Generalized Quasispecies Model on Finite Metric Spaces: Isometry Groups and Spectral Properties of Evolutionary Matrices, Journal of Mathematical Biology, 2019, 78(3), 837-878
- Bratus, A.S., Novozhilov, A.S. and Semenov, Y.S.: Rigorous mathematical analysis of the quasispecies model: From Manfred Eigen to the recent developments, in Advanced Mathematical Methods in Biosciences and Applications, Editors: Faina Berezovskaya and Bourama Toni, 2019
- Bratus, A.S., Novozhilov, A.S., Semenov, Y.S.: Adaptive Fitness Landscape for Replicator Systems: To Maximize or not to Maximize, Mathematical Modelling of Natural Phenomena, 2018, 13(3): 25
- Koonin, E.V., Novozhilov, A.S.: Origin and evolution of the universal genetic code, Annual review of genetics, 2017, 51: 45-62
- Bratus, A.S., Posvyanskii, V.P., Novozhilov, A.S.: Solutions with a bounded support promote permanence of a distributed replicator equation, Applicable Analysis, 2017, 96(15): 2652-2668
- Semenov, Y.S., Novozhilov A.S.: On Eigen's quasispecies model, two-valued fitness landscapes, and isometry groups acting on finite metric spaces, Bulletin of Mathematical Biology, 2016, 78(5): 991-1038
- Bratus, A.S., Hu, C.-K. Safro, M.V., and Novozhilov, A.S.: On diffusive stability of Eigen's quasispecies model, Journal
of Dynamical and Control Systems, 2016, 22(1):1-14
- Semenov, Y.S., Novozhilov A.S.: Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model, Mathematical Biosciences, 2015, 266:1-9
- Semenov, Y.S., Bratus, A.S., Novozhilov, A.S.: On the behavior of the leading eigenvalue of Eigen's evolutionary matrices, Mathematical Biosciences, 2014, 258:134-147
- Bratus, A.S., Novozhilov, A.S., Semenov, Y.S.: Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution,
Mathematical Biosciences, 2014, 256:42-57
- Bratus, A.S., Posvyanskii, V.P., Novozhilov, A.S.
Replicator equations and space, Mathematical Modelling of Natural Phenomena, 2014, 9(3): 47-67
- Novozhilov, A.S.: Epidemiological models with parametric
heterogeneity: Deterministic theory for closed populations, Mathematical
Modelling of Natural Phenomena, 2012, 7(3): 147-167
- Novozhilov, A.S., Posvyanskii, V.P., Bratus, A.S.: On the
reaction–diffusion replicator systems: Spatial patterns and asymptotic
behavior, Russian Journal of Numerical Analysis and Mathematical Modelling,
2012, 26(6):555-564
- Bratus, A.S., Posvyanskii, V.P., Novozhilov, A.S.: A note on the
replicator equation with explicit space and global regulation, Mathematical
Biosciences & Engineering, 2011, 8(3):659-676
- Karev, G.P., Novozhilov, A.S., Berezovskaya, F.S.: On the asymptotic
behavior of the solutions to the replicator equation. Mathematical Medicine
& Biology, 2011, 28(2):89-110, doi:10.1093/imammb/dqq006
- Bratus, A.S., Novozhilov, A.S., Platonov, A.P.: Dynamical Systems and
Models in Biology, Moscow: FizMatLit, 2010, 400 pages, in Russian, ISBN:
978-5-9221-1192-8
- Bratus, A.S., Posvyanskii, V.P., Novozhilov, A.S.: Existence and
stability of stationary solutions to spatially extended autocatalytic and
hypercyclic systems under global regulation and with nonlinear growth rates.
Nonlinear Analysis Series B: Real World Applications, 2010, 11(3):1897-1917,
doi:10.1016/j.nonrwa.2009.04.013
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Novozhilov, A.S., Koonin, E.V.: Exceptional error minimization in putative
primordial genetic codes. Biology Direct. 2009, 4(44),
doi:10.1186/1745-6150-4-44
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Koonin, E.V., Novozhilov, A.S.: Origin and evolution of the genetic code:
The universal enigma. IUBMB Life. 2009, 61(2), 99-111, doi:10.1002/iub.146
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Novozhilov A.S.: Heterogeneous Susceptibles–Infectives model: Mechanistic
derivation of the power law transmission function. Dynamics of Continuous,
Discrete and Impulsive Systems (Series A, Mathematical Analysis). 2009,
16(S1), Suppl., 136-140
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Berezovskaya, F.S., Karev, G.P., Novozhilov, A.S.: Pure cross-diffusion
models: Implications for traveling wave solutions. Dynamics of Continuous,
Discrete and Impulsive Systems (Series A, Mathematical Analysis) 2009, 16(S1),
Suppl., 141-146
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Novozhilov, A.S.: On the spread of epidemics in a closed heterogeneous
population. Mathematical Biosciences. 2008, 215, 177-185,
doi:10.1016/j.mbs.2008.07.010
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Berezovskaya, F.S., Novozhilov, A.S., Karev, G.P.: Families of traveling
impulses and fronts in some models with cross-diffusion. Nonlinear Analysis:
Real World Applications. 2008, 9: 1866-1881, doi: 10.1016/j.nonrwa.2007.06.001
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Karev, G.P., Novozhilov, A.S., Berezovskaya F.S.: Modeling the dynamics of
inhomogeneous natural rotifer populations under toxicant exposure. Ecological
Modeling. 2008, 212(1-2): 80-85, doi:10.1016/j.ecolmodel.2007.10.011
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Novozhilov, A.S., Wolf, Y.I., Koonin, E.V.: Evolution
of the genetic code: partial optimization of a random code for robustness to
translation error in a rugged fitness landscape. Biology Direct. 2007, 2(24),
doi: 10.1186/1745-6150-2-24
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Berezovskaya, F.S., Novozhilov, A.S., Karev, G.P.:
Traveling fronts, impulses and trains in some taxis models. Neural, Parallel
& Scientific Computations. 2007, 15: 561-570
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Berezovskaya, F.S., Novozhilov, A.S., Karev, G.P.: Population models with
singular equilibrium. Mathematical Biosciences. 2007, 208(1):270-299
- Karev,
G.P., Novozhilov, A.S., Koonin, E.V.: Mathematical modeling of tumor therapy
with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics.
Biology Direct. 2006, 1(1):30
Novozhilov, A.S.,
Berezovskaya, F.S., Koonin, E.V., Karev, G.P.: Mathematical modeling of tumor
therapy with oncolytic viruses: Regimes with complete tumor elimination within
the framework of deterministic models. Biology Direct. 2006, 1(1):6 -
Novozhilov, A.S., Karev, G.P., Koonin, E.V.:
Biological applications of the theory of birth-and-death processes. Briefings
in Bioinformatics. 2006, 7(1):70-85
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Novozhilov, A.S., Karev, G.P., Koonin, E.V.:
Mathematical modeling of evolution of horizontally transferred genes.
Molecular Biology and Evolution. 2005, 22(8):1721-1732
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Bratus, A.S., Novozhilov, A.S.: Stabilizing effect of
nonlinear damping for a system with follower force. Functional Differential
Equation. 2005, 12(1-2):109-118
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Novozhilov, A.S.: Analysis of a generalized population
predator-prey model with a parameter distributed normally over the individuals
in the predator population. Journal of Computer and Systems Sciences
International. 2004, 43(3):378-382
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Novozhilov, A.S.: Parameter identification for one
dynamical system that simulates the interaction of pollutants with the active
environment. Journal of Computer and Systems Sciences International. 2002,
41(3):433-436
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Bratus, A.S, Mescherin, A.N., Novozhilov, A.S.:
Mathematical models of interaction between pollutant and environment. Vestnik
MGU, Vychislitelnaya matematica i kybernetica. 2001, 1:23-28 (in
Russian)
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Novozhilov, A.S., Bratus, A.S.: Nonlinear damping as
a stabilizing factor and resolving Ziegler's paradox. Proceeding of the 5th
Symposium "Nonlinear Control and Oscillations"(NOLCOS'01), July, St.
Petersburg, Russia, 2001, 2:973-978
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Bratus, A.S., Mescherin, A.N., Novozhilov, A.S.:
Mathematical Models of Interaction between Pollutant and Environment.
Proceeding of the 2nd international conference "Control of Oscillations and
Chaos" (COC 2000), July, St. Petersburg, Russia, 2000, 3:569-57
PhD Thesis
- Novozhilov, A.S.: Mathematical models of interaction between pollutant and
environment. Thesis for Ph.D. degree in Applied Mathematics. Moscow:
Moscow State University of Communication Means (MIIT), 2002, 84 p. (in
Russian)
arXiv link
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