ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


dynamics

On the genetic divergence of two adjacent populations living in a homogeneous habitat

The purpose is to study the mechanisms leading to the genetic divergence, i.e. stable genetic differences between two adjacent populations coupled by migration of individuals. We considered the case when the fitness of individuals is strictly determined genetically by a single diallelic locus with alleles A and a, the population is panmictic and Mendel's laws of inheritance hold. The dynamic model contains three phase variables: concentration of allele A in each population and fraction (weight) of the first population in the total population size.

Dynamics of two-component parabolic systems of schrodinger type

Issue. The paper considers the local dynamics of important for applications class of two-component nonlinear systems of parabolic equations. These systems contain a small parameter appearing in the diffusion coefficients and characterizing «closeness» of the initial system of a parabolic type to a hyperbolic one. On quite natural conditions critical cases in the problem about balance state stability are realized to linearized equation coefficients. Innovation.

Asymptotic research of local dynamics of the Cahn–Hilliard family equations

Topic. Dynamics of well-known Cahn–Hilliard nonlinear equation is researched. In a state of balance stability task, critical cases were highlighted and bifurcation phenomena were researched. Aim. To formulate finite-dimensional and special infinite-dimensional equations, which can be represented as normal forms. Method. You can use as standard local dynamics research methods, based on constructing of normal forms on central manifolds, and special infinite-dimensional normalization ones.