Local dynamics of equation with periodically distributed delay

Theoretical and Mathematical Physics - We study an equation with periodically distributed delay. The dependence of the equilibrium state stability on the parameters is investigated. We show that...     

Local Dynamics of a Singularly Perturbed Second Order Equation with State-Dependent Delay

Mathematical Notes -     

Asymptotics of the Relaxation Cycle in the Modified Logistic Equation with Delay

Mathematical Notes -     

Dislocation centers in α-martensite formation and dual couplings of thinly-laminated martensite crystals

The spectrum of observable dual couplings of crystals of thinly-laminated martensite with habiti {3 15 10} is discussed within the framework of the concept of the dislocation formation of -martensite crystals. A spectrum of dislocation centers of formation arising together with the developing martensite crystal is proposed. Here it is essential to divide the arising dislocation centers of formation into two groups associated with different displacement mechanisms. This difference permits understanding of the difference in the frequency of observation of couplings and the introduction of the concept of a comb structure — a set of secondary parallel crystals of martensite, associated with the same initial crystal.Urals Forestry Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 64–67, June, 1994.     

The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.