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A secondary ion yield change from photoconducting semiconductors under influence of illumination has been established (secondary-ion photoeffect). The classification of this phenomenon is given: the normal and the anomalous secondary ion photoeffects are defined. The normal photoeffect is found in reducing of cadmium positive secondary ion yield from CdS-PbS sample under illumination as a result of electron work function decrease. The anomalous effect consists in increase of lead positive secondary ion yield from the same sample under illumination (up to 1200% about in dark).

It has been shown in this work how the evolutionary change of alleles’ frequencies, which is accompanied by the growth of average population fitness, leads to chaotic and cyclic dynamics of population size. Then the possible mechanisms of appearance of complicate temporal organization of genetic biodiversity have been considered.

The results of numerical simulation of oscillations in a simple model of interaction of waves with inertial nonlinearity applicable to study of phenomena in a backward wave oscillator are produced. Convenient numerical characteristics for identification of anharmonic oscillations – a decrement of the autocorrelation function and the characteristic correlation time – have been used. It has been found that both sophistication and ordering of an excited signal were possible under influence of additive noise.

The dynamics of a system with unstable limit cycle under the periodic sequence of delta-pulses 

is considered. It is shown, that stable quasi-periodic regimes and phase lock regimes 

(synchronization) are observed within a narrow range of parameters of the external action in the 

system with cubic nonlinearity. Influence of main system’s parameters to the stable quasi-

periodic regimes and phase lock regimes is investigated.

Analogy between an approximate version of period-doubling (and period N-tupling) renormalization group analysis in complex domain and the phase transition theory of Yang-Lee (based on consideration of formally complexified thermodynamic values) is discussed. It is shown that the Julia sets of the renormalization transformation correspond to the approximation of Mandelbrot set of the original map. New aspects of analogy between the theory of dynamical systems and the phase transition theory are uncovered.

On the basis of quasi-potential method the stationary distribution of random trajectories in a vicinity of toroidal manifolds of stochastically forced nonlinear systems is investigated. For the quasi-potential approximation the quadratic form defined by some matrix function is used. This function named stochastic sensitivity function characterizes the response of considered system on random disturbances. Construction of this function is reduced to the decision of a boundary problem for linear differential matrix equation.

Dynamics of an ensemble of two parallel phase-locked-loop systems with lowinertia control loops is investigated. Stability of synchronous modes of the ensemble is considered. Mechanisms of arising of quasi-synchronous oscillations are studied. Domains of existence of synchronous, quasi-synchronous, and asynchronous modes are analysed. The results obtained are compared with analogous data of modeling dynamics of an ensemble with cascade coupling; their common features and basic differences are distin- guished.

The article is devoted to historical development of one key aspect of Hamiltonian systems – nonintegrability, and its relation with chaotic behavior of the system. Evolution from the concept of quite integrable system to partly integrable one is shown. The relation of nonintegrability with such fundamental concepts as Kolmogorov stability, systems with divided phase space, Arnold diffusion, Zaslavsky web and others is discussed.

Different methods for investigation of dissipative, nearly conservative and conservative systems have been demonstrated on the example of Ikeda map. The method for two-parameter analysis of dynamics of conservative systems has been proposed. Significant changes in the structure of the parameter and phase space of Ikeda map when dissipation decreases have been revealed. Tasks for seminars and computer practices have been proposed.

This paper is the book review. Its main purpose is to show that practically all kinds of canonical models of nonlinear dynamics are used in the present mathematical economics.