arXiv subjects

Sergey Vakulenko

Publications and source records attributed to Sergey Vakulenko.

7 recordsLinked to original sources

arXiv2019

Strange attractors for Overbeck -Boussinesq model

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 stable dynamics defined by $C^1$ smooth vector fields on compact smooth manifolds (up to an orbital topological equivalency). To generate a prescribed dynamics, it is sufficient to adjust some parameters in the equations, namely, the viscosity coefficient, an external heat source, some parameters in boundary conditions and the small perturbation of the gravitational force.

math-ph↗

arXiv2018

Biodiversity and robustness of large ecosystems

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 extinction threshold is distinct from zero, the large time dynamics of system is fundamentally non-predictable. In the last part of the paper we obtain explicit analytical estimates of ecosystem robustness with respect to variations of resource supply which support the $R^*$ rule for a system with random parameters.

math.DS↗

arXiv2017

Global stability and persistence of complex foodwebs

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.

math.DS↗

arXiv2016

Gene networks accelerate evolution by fitness landscape learning

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 expression. We show that this regulation is very powerful: depending on parameters we can obtain any functional connection between thresholds and genes. Under general 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 the number of mutations necessary for adaptation and thus accelerates of evolution. Moreover, this learning increases phenotype robustness with respect to mutations. However, this acceleration leads to an additional risk since learning procedure can produce errors. Finally evolution acceleration reminds races on a rugged highway: when you speed up, you have more chances to crash. These results explain recent experimental data on anticipation of environment changes by some organisms.

q-bio.PE↗

arXiv2016

Complex bifurcations in Bénard-Marangoni convection

We study the dynamics of a system defined 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 a certain nonlinear temperature profile as compared to bifurcations in the classical Rayleigh-Bénard and Bénard-Marangoni systems with simple linear vertical temperature profiles. In terms of the Bénard-Marangoni convection, the obtained mathematical results lead to our understanding of complex spatial patterns at a free liquid surface, which can be induced by a complicated profile of temperature or a chemical concentration at that surface. In addition, we discuss some possible applications of the results to turbulence theory and climate science.

math-ph↗

arXiv2015

New perspectives: stability and complex dynamics of food webs via Hamiltonian methods

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, interaction structure and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and investigate how these phenomena depend on ecological interaction structure. We show that a Hamiltonian structure of interaction leads to stability and large biodiversity.

math.AP↗

arXiv2013

A hybrid mammalian cell cycle model

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, and rapid changes of regulatory proteins concentrations induced by post-translational modifications. The advancement through the cell cycle comprises a well defined sequence of stages, separated by checkpoint transitions. The combination of continuous and discrete changes justifies hybrid modelling approaches to cell cycle dynamics. We present a piecewise-smooth version of a mammalian cell cycle model, obtained by hybridization from a smooth biochemical model. The approximate hybridization scheme, leading to simplified reaction rates and binary event location functions, is based on learning from a training set of trajectories of the smooth model. We discuss several learning strategies for the parameters of the hybrid model.

cs.CE↗