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Mathematical model of ion fluxes across the cell membrane of algae Chara coralline is developed. The transient processes and self-oscillating modes connected with potential-dependent transport of protons across the membrane are considered. Important role ofthese processes for plant cell is discussed.

This paper demonstrates a tool for prediction time series on a base of iterated function system of the theory of fractals. Iterations result in an attractor or fractal in a space of compacts. The attractor is a support of invariant probabilistic measure or multifractal in a space of Borel measures. An inverse problem consists of finding iterated function system and its probabilities by means of empirical measure. The estimates might be obtained from time series by symbolic dynamics methods.

Книга вводит школьника и студента младшего курса в «творческую лабораторию» физика-исследователя. В форме задач она знакомит с «неформальной» физикой, которая связана с окружающим миром. Представлены задачи на оценки физических величин, методы размерностей и подобия, задачи для решения с помощью компьютера. Представлены также задачи исследовательского характера, которые могут быть использованы в рамках школьной научной лаборатории. Книга будет полезна школьникам, интересующимся физикой и исследовательской работой, а также учителям физики и студентам младших курсов.

The unusual technique of interpretation of numerical experiment results as sound waves is offered. Recommendations for practical implementation of the offered technique and for its application in various areas of research, designer and educational activity are given.

The property of unstable manifold of the Lorenz-system zero equilibrium is proved. This permited to prove the sufficient condition of homoclinic orbit existence.

By the way of combined integrating of the motion and variation equations we calculated the maximal characteristic Lyapunov exponents in the wide limits of energy and time for the Henon–Heiles problem. It follows from the fitting procedure that the best approximate function is the exponential one with the parameter values, which are different from the earlier obtained parameter values (Benettin et al.).

In the frame of a model given before for simulation of chaotic dynamics of continuum medium the Lorenz attractor is represented. The simulation is given with the help of the structures that define the geometry of a fiber bundle associated with 3-dimensional regime of velocity pulsations. Lorenz dynamics appears as time dependence of pulsations along the lines of average flow.

The paper studies the chaotic dynamics in circular asymmetric billiard with beams reflection and refraction. Phase dynamics is characterized by a variety of dynamics modes, which is connected with the effect of traditional chaotization mechanisms as well as with the complicacy of allowable motion laws. In the multisheet symmetric phase space, the circular billiard reconstructions have been analysed its asymmetry degrees changes.

Chaotic RF generator with bipolar transistor is proposed. Mathematical model of  the generator, oscillator with 2.5 degrees of freedom, is investigated. Generator dynamics is analyzed with Advanced Design System (ADS) software using parameters of a real transistor, properties of the board substrate are taken into account by simulation. ADS simulation results are compared with experimental data. It is shown that the use of ADS software for analysis of generator dynamics and account for the board properties and topology allow to get simulation results closer to the experimental one.

We present the analysis of spatiotemporal dynamics in the system modeling collective behaviour of ensemble of electrically coupled neuronal cells. The dynamics of local element is described by the FitzHugh – Nagumo system with complex threshold excitation. Heteroclinic orbits and corresponding wave fronts are investigated. We show that in the phase space of system for traveling waves there exist heteroclinic cycle formed by separatrix manifolds of two saddle-foci.