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


бифуркации

Simple and complex dynamics in the model of evolution of two populations coupled by migration with non-overlapping generations

Purpose is to study the mechanisms leading to genetic divergence (stable genetic differences between two adjacent populations). We considered the following classical model situation. Populations are panmictic with Mendelian rules of inheritance. The action of natural selection (differences in fitness) on each of population is the same and is determined by the genotypes of only one diallel locus. We assume that adjacent generations do not overlap and genetic transformations can be described by a discrete time model.

Простая и сложная динамика в модели эволюции двух миграционно связанных популяций с непересекающимися поколениями

Цель работы – исследование механизмов, приводящих к возникновению генетической дивергенции (устойчивых генетических различий между двумя популяциями, связанными миграцией). Рассматривается «классическая» модельная ситуация: панмиктичные популяции с менделевскими правилами наследования, в которых действие естественного отбора (различия по приспособленностям) одинаково и определяется генотипами только одного диаллельнго локуса. Предполагается, что смежные поколения не перекрываются и эволюционные преобразования можно отслеживать моделью с дискретным временем.

Cycles-canards and torus-canards in a weakly inhomogeneous ensemble of FitzHugh–Nagumo neurons with excitatory synaptic couplings

The purpose of this work is to study the dynamics of a weakly inhomogeneous ensemble of three FitzHugh–Nagumo neurons with excitatory synaptic couplings. To single out main types of canard solutions of the system and obtain the regions in parameter space the solutions exist in. Methods. In this paper the dynamics of autonomous systems are studied by using methods based on geometric singular perturbation theory. To study the dynamics of non-autonomous systems we develop an approximate approach and use numerical methods such as obtaining of Poincare maps. Results.

Циклы-утки и торы-утки в слабо-неоднородном ансамбле нейронов ФитцХью-Нагумо с возбуждающими синаптическими связями

Цель настоящего исследования - изучить динамику слабо-неоднородного ансамбля из трех нейронов ФитцХью-Нагумо с синаптическими возбуждающими связями. Установить основные типы наблюдаемых в такой системе уточных решений и выявить области в пространстве параметров, отвечающие существованию этих решений. Методы. В данной работе для изучения динамики автономных систем применяются аналитические методы, основанные на геометрической теории сингулярных возмущений.

Equations with the Fermi–Pasta–Ulam and dislocations nonlinearity

Issue. The class of Fermi–Pasta–Ulam equations and equations describing dislocations are investigated. Being a bright representative of integrable equations, they are of interest both in theoretical constructions and in applied research. Investigation methods. In the present work, a model combining these two equations is considered, and local dynamic properties of solutions are investigated. An important feature of the model is the fact that the infinite set of characteristic numbers of the equation linearized at zero consists of purely imaginary values.

УРАВНЕНИЯ С НЕЛИНЕЙНОСТЯМИ ДИСЛОКАЦИЙ И ФЕРМИ-ПАСТА-УЛАМА

Тема и цель исследования. Исследуется класс уравнений Ферми-Паста-Улама и уравнений, описывающих дислокации. Этим уравнениям посвящено большое число работ. Эти уравнения представляют определенный интерес и в прикладном смысле, и в теоретических исследованиях, являсь ярким представителем интегрируемых уравнений. Исследуемые модели. В предыдущей работе была рассмотрена модель, объединяющая эти два уравнения и изучен ряд вопросов, касающихся интегрируемости по Пенлеве её решений.

Bifurcations of one-parameter families of steady state regimes in model of a filtrational convection

Results of numerical investigation of bifurcations of one-parameter families of steady state regimes in a planar filtrational convection problem are presented. Galerkin’s method is applied for approximation of partial differential equations. As a result of the cosymmetry existence there are curves of equilibria with the hidden parameter. The algorithm of calculation of such curves is described. This algorithm can be applied to analyze systems with nonisolated sets of equilibria.

Subharmonic resonance in a system of two dissipative coupled van der Pol oscillators with external force

The problem of the excitation of two coupled oscillators is discussed in the case of the simple subharmonic resonance between the external force and eigen-frequencies of the oscillators. The corresponded phase equation is obtained. We showed that the form of the synchronization tongue and transformation of the region of the two-, three-frequency tori by varying the parameter of the coupling between the oscillators is significantly different from the case of the main resonance.

Dynamics of two nonlinearly coupled nonidentical Lang–Kobayshi oscillators

One-parameter study of system of two nonlinearly coupled nonidentical Lang– Kobayshi oscillators is presented. The time delay influence on oscillation regimes in the system is studied. The posibility of periodic and quasiperiodic oscillations is shown. Variation of delay time leads to bifurcations and an alternation of periodic and quasiperiodic oscillations. Quasiperiodic oscillations are excited as a result of Neimark–Sacker bifurcation.

New type of bifurcations in the modified Rayleigh–Benard convection problem

The original Rayleigh–Benard convection is a standard example of the system where bifurcations occur with changing of a control parameter. In this paper we consider the modified Rayleigh–Benard convection problem including radiative effects as well as gas sources on a surface. Such formulation leads to the identification of new type of bifurcations in the problem besides the well-known Benard cells.

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