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


nonlinearity

Human brain state monitoring in perceptual decision-making tasks

The purpose of this review is to observe the current state of research on sensorimotor integration in the human brain during visual perception and subsequent decision-making under conditions of ambiguous information. Methods. This review examines the approaches of time-frequency wavelet analysis for brain activity when performing perceptual tasks, as well as the possibility of using such methods in the tasks of constructing brain – computer interfaces. Results.

Mathematical model and dynamical analysis of the human equilibrium seeking training

The purpose of this work is to determine the ability of the partial directed coherence method to identify the
directed interaction between nonlinear systems correctly in presence of nonlinear couplings between systems, as well as
in the case when the measured signals are generated by objects of high dimension. The another purpose is to determine
the dependence of the coupling estimation results on the parameters: series length, sampling rate, model dimension and the

Non-contact atomic force microscope: Modeling and simulation using van der Pol averaging method

Topic and aim. One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. This work aimed at creating the mathematical model of the non-contact atomic force microscope. Models and Methods.

Non-Contact Atomic Force Microscope: Modeling and Simulation using Van der Pol Averaging Method

One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. The lumped parameter model of the atomic force microscope in the non-contact operation mode is utilized to make the mathematical model of the micro cantilever of the AFM in this article.

Waves of strain in two coaxial cubically nonlinear cylindrical shells with a viscous fluid between them

Subject of the study. Longitudinal deformation waves are investigated in physically nonlinear coaxial elastic shells with a viscous incompressible fluid between its. There are taken into account effect on the amplitude and speed of inertia wave of the fluid and the environment, and as well as the damping properties of the structural materials, from which the waveguides are made.

Multistability and memory effects in dynamical system with cosymmetric potential

The purpose of present study is the analysis of strong multistability in a dynamical system with cosymmetry. We study the dynamics and realization of steady-states in a mechanical system with two degrees of freedom. The minimum potential energy of the system is achieved on a curve in the form of an ellipse, which gives rise to a continuum family of equilibria and strong multistability. This problem belongs to the class of dynamical systems with cosymmetry. Methods.

Effect of nonlinearity on coupling estimations between oscillators using partial directed coherence approach

The purpose of this work is to determine the ability of the partial directed coherence method to identify directed interactions between nonlinear systems correctly in presence of nonlinear couplings between systems, as well as in the
case of measured signals generated by objects of high dimension. The other purpose is to determine the dependence of the coupling estimation results on the parameters: series length, sampling rate, model dimension and coupling architecture.

Sergey P. Kurdyumov and his evolutionary model of dynamics of complex systems

Sergei P. Kurdyumov (1928–2004) and his distinguished contribution in the development of the modern interdisciplinary theory and methodology of study of complex selforganizing systems, i.e. synergetics, is under consideration in the article. The matter of a mathematical model of evolutionary dynamics of complex systems elaborated by him is demonstrated. The nonlinear equation of heat conductivity serves as a basis of the model. Under certain conditions, it describes dynamics of development of structures of different complexity in the blow-up regime.

Nonlinear models of blood supply dynamics in tissue area

A continual model of tissue blood supply has been suggested in this paper providing the existence of autostructures in the inhomogeneous blood distribution. Theoretical analysis including both analytical and numerical calculations has been carried out on the base of this model. The filtration variations of blood flow caused by medium activity (chemical reactions, nerve excitation) have been studied as well as self-organization processes accounting mechanisms of microvessel regulation.

Radial patterns in a vibrated granular layer

Laboratory experiments were conducted for a sand layer placed in the verticallyoscillated containers of various shapes. Radial patterns on the sand surface were observed; experimental investigations of such structures have never been described in scientific literature. The waveform, amplitude and frequency of vibrations and the depth of the vibrated layer could be varied, allowing study the dependence of the shape and scale of radial structures upon these parameters.