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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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)

• 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

• 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

• Papers at arXiv