Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator.

Transition to chaos via the destruction of a two-dimensional torus is studied numerically using an example of the Hénon map and the Toda oscillator under quasiperiodic forcing and also experimentally using an example of a quasi-periodically excited RL-diode circuit. A feature of chaotic dynamics in these systems is the fact that the chaotic attractor in them has an additional zero Lyapunov exponent, which strictly follows from the structure of mathematical models. In the process of research, the influence of feedback is studied, in which the frequency of one of the harmonics of external forcing becomes dependent on a dynamic variable. Charts of dynamic regimes were constructed, examples of typical oscillation modes were given, and the spectrum of Lyapunov exponents was analyzed. Numerical simulations confirm that chaos resulting from the cascade of torus doubling has a close to the zero Lyapunov exponent, beside the trivial zero exponent.

Smale-Williams solenoids in autonomous system with saddle equilibrium.

We construct an autonomous low-dimensional system of differential equations by replacement of real-valued variables with complex-valued variables in a self-oscillating system with homoclinic loops of a saddle. We provide analytical and numerical indications and argue that the emerging chaotic attractor is a uniformly hyperbolic chaotic attractor of Smale-Williams type. The four-dimensional phase space of the flow consists of two parts: a vicinity of a saddle equilibrium with two pairs of equal eigenvalues where the angular variable undergoes a Bernoulli map, and a region which ensures that the trajectories return to the origin without angular variable changing. The trajectories of the flow approach and leave the vicinity of the saddle equilibrium with the arguments of complex variables undergoing a Bernoulli map on each return. This makes possible the formation of the attractor of a Smale-Williams type in Poincaré cross section. In essence, our model resembles complex amplitude equations governing the dynamics of wave envelops or spatial Fourier modes. We discuss the roughness and generality of our scheme.

[Dependence of the intensity of growth processes on the potential difference at the cytoplasmic membrane]. / Zavisimost' intensivnosti rostovykh protsessov ot raznosti potentsialov na tsioplazmaticheskoi membrane.

The growth of organisms is a dynamic process of interrelated fluxes of substances and energy which most often proceeds in the steady-state conditions, the energy-dependent process being predominant. The rate of growth is directly proportional to the potential difference at the plasma membrane, created essentially by a passive influx of energy substance to the cell oxidative system which is a limiting link of its energization. The formation of potential difference is influenced by concentrations of biomass and energy substrate at the plasma membrane, as well as the values of electric capacity of the membrane and rate constants for the electric charge formation and expenditure.

[Resolution of the fluorescence and absorption spectra of chlorophyll a in the cell into its components]. / Razlozhenie na komponenty spektrov fluorestsentsii i pogloshcheniia khlorofilla a v kletke.

The total number, band widths, absorption and fluorescence peak positions of universal forms of chlorophyll a in vivo were identified by means of computer curve analysis, Stepanov's relation and low temperature derivative spectroscopy. The identified pigment forms are as follows: Chl669(661), Chl676(674), Chl686(680), Chl691(687), Chl697(691), Chl706(698), Chl715(702) Chl726(709), Chl738(715) and Chl750--755(720--724) (the lower index--absorption peak position, the upper one--fluorescence peak position). The O--O electronic transitions vibronic bands energy one of the forms of chlorphyll alpha enumerated above changes for constant equal 140 cm--1.