Applied Problems of Nonlinear Oscillation and Wave Theory

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.

Topic. The paper is devoted to the analysis of the dynamics of a complex system, i.e. a hinge mechanism plus a compound pendulum, in which where a differential equation is found, describing its nonlinear behavior.

Theme – the effect of symmetry violation on the structure of the phase space of invertible systems. Aim – to study the changes in the phase space structure of invertible systems caused by the violation of symmetry, in particular, the possibility of multistability and the types of coexisting attractors.

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.

Topic. The subject of the article is the expansion of the author’s research series in the direction of mathematical modeling of specific ecological situations and transitional regimes that arise in nonlinear population processes with complex internal regulation.

Purpose. The aim is to reveal the dependence of Granger causality results on chosen time scales of constructed empirical models in application to the task of investigation of evolution of coupling between brain areas during limbic seizures.

Aim. The aim of the investigation is to study the evolutionary properties changes of the dynamic cutting system and the bifurcation of the attracting sets of the deformation displacement of the tool due to the irreversible transformation of the energy input in coupling tool-processing are considered.

Subject of the study. Excitable dynamic systems are the systems having a stable equilibrium and capable of generating a large amplitude response to a weak stimulation. Excitable dynamic systems research is one of the most interesting and actual problems of modern nonlinear science. In the present paper dynamics of phase-locked loop with bandpass filter is studied under external pulse stimulation. Novelty.

Topic. Based on the assumption that short-term climatic variations are nonchaotic, and, therefore, the paradigm of the limited predictability of weather formulated by E.N. Lorenz is not applicable to these variations, a question is posed about the unlimited predictability of the short-term climatic variations.

A mathematical model with 2.5 degrees of freedom under external periodic stimulation is investigated. It is a model of chaotic oscillator with bipolar transistor as an active element. It is shown that external periodic stimulation of the oscillator of such system allows to generate chaotic pulse stream.

DOI: 10.18500/0869-6632-2015-23-2-37-46