# Sergey VakulenkoRussian Academy of Sciences | RAS

Sergey Vakulenko

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166

Publications

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Introduction

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## Publications

Publications (166)

This paper presents a mathematical analysis of an extended model describing a sea ice-induced frequency lock-in for vertically sided offshore structures. A simple Euler–Bernoulli beam as model for the offshore structure is used, and a moving boundary between an ice floe and the structure itself is introduced. A nonlinear equation for the beam dynam...

Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species extinctions. There are population dynamic models that describe a simple and easily understandable mechanism for resour...

In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of...

In this paper, we consider dynamics defined by the Navier–Stokes equations in the Oberbeck–Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involves fundamental physical effects: convection, and diffusion. The main result is as follows: local semiflows, induced by this problem, can generate all possible structurall...

With the growing number of discovered exoplanets, the Gaia concept finds its second wind. The Gaia concept defines that the biosphere of an inhabited planet regulates a planetary climate through feedback loops such that the planet remains habitable. Crunching the “Gaia” puzzle has been a focus of intense empirical research. Much less attention has...

Asymptotic solutions for two cases of the problem on finite numbers of impacts on a membrane are obtained: 1. the case of a small damage function values of the membrane elastic foundation, and 2. the case of significant damage function values of its elastic foundation. A condition of resonance initiation in the membrane with a small damage function...

We consider centralized networks composed of multiple satellites arranged around a few dominating super-egoistic centers. These so-called empires are organized using a divide and rule framework enforcing strong center–satellite interactions while keeping the pairwise interactions between the satellites sufficiently weak. We present a stochastic sta...

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on wheth...

Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species extinctions. There are population dynamics models that describe a simple and easily understandable mechanism for resou...

The paper considers the problem of parameter identification of the surface mounted permanent magnet synchronous motor (SPMSM) with pulse width modulated (PWM) inverter in the presence of dead time of power switches and other nonlinear distortions. Parameter identification of the SPMSM is required for the tuning of the torque control loop, because i...

In this paper, a new simple oscillator model is considered describing ice-induced vibrations of upstanding, water-surrounded, and bottom-founded offshore structures. Existing models are extended by taking into account deformations of an ice floe and a moving contact interaction between an ice rod, which is cut out from the floe, and the oscillator...

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. Under some assumptions on fitness we prove that such model organisms are capable, to some extent, to recognize the fitness landscape. That fitness landscape learning sharply reduces t...

In this paper, we consider effects of impurity diffusion and convection in strained elastic materials with the help of a two-component continual model, that takes into account change in the rigid properties of the material. Two new kinds of solutions, which describe propagation of localized waves, have been found. The first type of solutions descri...

We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalize some previous works and takes into account self-limitation. Under certain conditions, we establish the global convergence and persistence of solutions.

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. Under some assumptions on fitness we prove that such model organisms are capable, to some extent, to recognize the fitness landscape. That fitness landscape learning sharply reduces t...

We consider a class of quadratic systems with slow and fast variables, which exhibit complicated bifurcations when the dynamic parameter (physically interpreted as the load on a system) is changing. We prove that this system with any two different structurally stable dynamical regimes bifurcates from the first regime to the second one as a result o...

In this paper, we consider dynamics defined by the Navier-Stokes equations in the Oberbeck-Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involve fundamental physical effects: convection, and diffusion. The main result is as follows: local semiflows, induced by this problem, can generate all possible structurally...

In this paper a new simple oscillator model is considered describing ice induced vibrations of upstanding, water surrounded, and bottom-founded offshore structures. Existing models are extended by taking into account deformations of an ice floe, and a moving contact interaction between an ice rod, which is cut out from the floe, and the oscillator...

Numerous experimental studies on shock wave loading of metals have shown by electron microscopy that the crystal structure of the material can undergo transformation in a certain impactor velocity range. At the macroscale, these changes are observed as energy losses associated with the formation of a new structure. The losses are manifested on the...

We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the global stability of solutions for systems with extinctions and large turnover rate. We show that when the extinc...

We consider semiflows generated by initial boundary value problems for reaction–diffusion systems. In these systems, reaction terms satisfy general conditions, which admit a transparent chemical interpretation. It is shown that the semiflows generated by these initial boundary value problems exhibit a complicated large time behavior. Any structural...

In this paper, we study a model of many species that compete, directly or indirectly, for a pool of common resources under the influence of periodic, stochastic, and/or chaotic environmental forcing. Using numerical simulations, we find the number and sequence of species going extinct when the community is initially packed with a large number of sp...

To mathematically show the existence and stability of large foodwebs, large and complex as foodwebs in nature, is still one of the key problems in theoretical ecology. A specific part of this theoretical issue is that many species can share just a few resources, yet the competitive exclusion principle asserts that such foodwebs should not exist. To...

We propose a simple 3-parameter model that provides very good fits for incidence curves of 18 common solid cancers even when variations due to different locations, races, or periods are taken into account. From a data perspective, we use model selection (Akaike information criterion) to show that this model, which is based on the Weibull distributi...

We consider continuous-time recurrent neural networks as dynamical models for the simulation of human body motions. These networks consist of a few centers and many satellites connected to them. The centers evolve in time as periodical oscillators with different frequencies. The center states define the satellite neurons' states by a radial basis f...

The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such models to provide quantitative formalization of changes to Earth's biosphere. In this paper we propose and st...

The prevailing heat transfer processes—convection in the photosphere and wave propagation in the chromosphere—are principally different. Despite this fact, there is a direct link between these processes: it is precisely convective photospheric flows that excite intense Alfven waves in the chromosphere. A physical model explaining the effect of stro...

The dynamics of a string on an elastic foundation with time- and coordinate-dependent coefficients have been studied. Asymptotic solutions have been constructed for the following cases: for an arbitrary value of the elastic foundation coefficient at small and large time values, and for small and large coefficients of the elastic foundation at arbit...

We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species and find a relation describing how many species that may go extinct as a result of a sharp enviro...

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently th...

This paper considers a model of foodwebs taking into account species extinction and invasion. We show that system stability depends not only on usual parameters (mortality rates, self-limitation coefficients, and resource abundances), but also on an additional parameter (“biodiversity potential”). The main result is as follows. For foodwebs with ra...

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. We propose a new model of gene regulation, where gene expression is controlled by a gene network with a threshold mechanism and there is a feedback between that threshold and gene exp...

Asymptotic solutions of the problem of dynamics of an infinitely long string lying on an elastic base with prescribed damage under the action of finitely many periodic impacts are constructed in the two cases of small and large damage of the elastic base. The condition of resonance origination in the string is obtained in the case of small damage w...

We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of N
s
weakly connected satellites, a property that we call n/N
s
-centrality. If the hub dynamics is slow, we obtain that the...

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations bet...

We study the dynamics of a system as determined by the Navier-Stokes
equations for a non-compressible fluid with Marangoni boundary conditions in
the two dimensional case. We show that more complicated bifurcations can appear
in this system for some nonlinear vertical temperature profile as compared to
bifurcations in classical Rayleigh-B\'enard an...

The dynamics defined by the Navier-Stokes equations under the Marangoni
boundary conditions in a two dimensional domain is considered. This model of
fluid dynamics involve fundamental physical effects: convection, diffusion and
capillary forces. The main result is as follows: local semiflows, defined by
the corresponding initial boundary value prob...

We investigate global stability and dynamics of large ecological networks by
classical methods of the dynamical system theory, including Hamiltonian
methods, and averaging. Our analysis exploits the network topological
structure, namely, existence of strongly connected nodes (hubs) in the
networks. We reveal new relations between topology, interact...

We discuss a method of approximate model reduction for networks of
biochemical reactions. This method can be applied to networks with polynomial
or rational reaction rates and whose parameters are given by their orders of
magnitude. In order to obtain reduced models we solve the problem of tropical
equilibration that is a system of equations in max...

We consider systems of differential equations with quadratic nonlinearities having applications for biochemistry and population dynamics, which may have a large dimension n. Due to the complexity of these systems, reduction algorithms play a crucial role in study of their large time behavior. Our approach aims to reduce a large system to a smaller...

We consider a class of systems of differential equations with quadratic nonlinearities. This class describes important biochemical models. We show that systems of this class can realize any structurally stable dynamics. Given a low dimensional dynamics, we describe algorithms that allow to realize this dynamics by a large biochemical network. Some...

Estimates of the number of local attractors for the Hopfield model of attractor neural network with continuous time and states where the neuron interaction graph has a scale-free structure are considered. The number of local attractors defines the network capacity, which is an important network characteristic. Numerous works were devoted to the pro...

We investigate a Lotka-Volterra model for a plankton ecosystem with a single
resource, self-limitation effects, and parameters depending on climate states
such as temperature. Analytical investigation and numerical simulations show
that the stochastic dynamics of this system exhibit strong dependence on
initial parameters. A range of situations wer...

In this paper, we show that oscillations of an Euler-Bernoulli beam with a small rigidity and with a time varying mass can lead to a resonance, which involves a large number of modes. This effect can induce a stability loss. The corresponding equations are complicated, in particular, in the nonlinear case with an external excitation. To analyze the...

This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important eleme...

The permafrost methane emission problem is the focus of attention on different climate models. Here, we present a mathematical
model for permafrost lake methane emission and its influence on the climate system. We model this process using the theory
of non-linear phase transitions. Further, we find that a climate catastrophe possibility depends on...

Understanding how sea ice melts is critical to climate projections. In the
Arctic, melt ponds that develop on the surface of sea ice floes during the late
spring and summer largely determine their albedo $-$ a key parameter in climate
modeling. Here we explore the possibility of a simple sea ice climate model
passing through a bifurcation point $-$...

The present paper is devoted to an issue of possible localization of waves propagating within a structure that consists of a film connected to a backing material by a substrate. The substrate is initially damaged. In the first approximation, the film model in the present paper is assumed to be a string on an elastic foundation with a coefficient de...

Hybrid modeling provides an effective solution to cope with multiple time
scales dynamics in systems biology. Among the applications of this method, one
of the most important is the cell cycle regulation. The machinery of the cell
cycle, leading to cell division and proliferation, combines slow growth,
spatio-temporal re-organisation of the cell, a...

In this paper, we study Lotka–Volterra systems with N species and n resources. We show that the long time dynamics of these systems may be complicated. Depending on parameter choice, they can generate all types of hyperbolic dynamics, in particular, chaotic ones. Moreover, Lotka–Volterra systems can generate Lorenz dynamics. We state the conditions...

We present a brief biographical review of the scientific work and achievements of Vladimir M. Shelkovich on the occasion of his sudden death in February 2013.

We propose a generalization of the classical Goody model by taking into account greenhouse gas emission effects. We develop an asymptotic approach that allows us to obtain an expression for the greenhouse gas flux via the temperature and fluid fields. We show that there is a possible tipping point in atmospheric dynamics resulting from greenhouse g...

Systems biology uses large networks of biochemical reactions to model the
functioning of biological cells from the molecular to the cellular scale. The
dynamics of dissipative reaction networks with many well separated time scales
can be described as a sequence of successive equilibrations of different
subsets of variables of the system. Polynomial...

We consider asymptotic solutions for nonlinear beams that can be described by a fourth order hyperbolic equation with an integral nonlinearity and some space and time dependent coefficients. These coefficients can describe varying mass and rigidity perturbations. A two-time scales perturbation method reduces this complicated equation to an infinite...

In the process of deformation of such multilayer structures, significant stresses can arise on the foundation-coating interface because of the difference in their physical and mechanical properties, which can result in fracture or coating separation. The action of static or impact loads on damage onset and development in the adhesive layer in such...

Piecewise smooth hybrid systems, involving continuous and discrete variables,
are suitable models for describing the multiscale regulatory machinery of the
biological cells. In hybrid models, the discrete variables can switch on and
off some molecular interactions, simulating cell progression through a series
of functioning modes. The advancement t...

This paper considers specially organized networks of large size. They can serve as models of computer communication systems, economical systems, neural and genetic networks. The topology of this network is simple and the analysis of the network behaviour is an analytically tractable task, while computer simulations are difficult. The authors show t...

We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact with one another via many u-nodes, called satellites. This centralized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable of generating practically...

The permafrost methane emission problem is in the focus of attention of
different climate models. We present new approach to the permafrost
methane emission modeling. The tundra permafrost lakes is potential
source of methane emission. Typically, tundra landscape contains a
number of small lakes and warming leads to lake extension. We are making
us...

Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial...

We consider networks with two types of nodes. The v-nodes, called centers,
are hyperconnected and interact one to another via many u-nodes, called
satellites. This centralized architecture, widespread in gene networks, realize
a bow-tie scheme and possesses interesting properties. Namely, this
organization creates feedback loops that are capable to...

We use the Litvinov-Maslov correspondence principle to reduce and hybridize
networks of biochemical reactions. We apply this method to a cell cycle
oscillator model. The reduced and hybridized model can be used as a hybrid
model for the cell cycle. We also propose a practical recipe for detecting
quasi-equilibrium QE reactions and quasi-steady stat...

This paper analyzes dynamical behavior of a simply supported Euler–Bernoulli beam with a time-varying mass on its surface.
Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal
resonances. The asymptotical solutions for the beam displacement has been found by combining the cl...

We consider a system of coupled oscillators. The system energy can be stabilized by different control mechanisms, for example, by a hybrid feedback control. We describe a constructive method to synchronize this system. It is shown that the synchronization is possible after stabilization of the system energy, even in a noisy environment.

We discuss piecewise smooth hybrid systems as models for regulatory networks in molecular biology. These systems involve both continuous and discrete variables. The discrete variables allow to switch on and off some of the molecular interactions in the model of the biological system. Piecewise smooth hybrid models are well adapted to approximate th...

We discuss piecewise smooth hybrid systems as models for regulatory networks in molecular biology. These systems involve both continuous and discrete variables. The discrete variables allow to switch on and off some of the molecular interactions in the model of the biological system. Piecewise smooth hybrid models are well adapted to approximate th...

We consider random-parameter chemical kinetic systems that are important in numerous physical, chemical, and biological applications.
Random parameters describe the action of ambient medium fluctuations on the system. We estimate the probability that the system
state remains in a given domain of the phase space during a time interval [0, T] under t...

We consider the viability problem for random dynamical systems, in particular, for circuits. A system is viable only if the system state stays in a prescribed domain Π of a phase space. We assume that the circuit structure is coded by a code evolving in time. We introduce the notion of stable evolution of the code and the system: evolution is stabl...

We propose a new mechanism for robust biological patterning. The mechanism bears analogy to interface dynamics in condensed media. We apply this method to study how gene networks control segmentation of Drosophila. The proposed model is minimal involving only 4 genes and a morphogen gradient. We discuss experimental data for which developmental gen...