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


Review of Actual Problems of Nonlinear Dynamics

«Exotic» models of high-intensity wave physics: linearizing equations, exactly solvable problems and non-analytic nonlinearities

Topic and aim. A brief review of publications and discussion of some mathematical models are presented, which, in the author’s opinion, are well-known only to a few specialists. These models are not well studied, despite their universality and practical significance. Since the results were published at different times and in different journals, it is useful to summarize them in one article. The goal is to form a general idea of the subject for the readers and to interest them with mathematical, physical or applied details described in the cited references. Investigated models.

Nonlinear dynamical models of neurons: review

Topic. A review of the basic dynamical models of neural activity is presented and individual features of their behavior are discussed, which can be used as a basis for the subsequent development and construction of various configurations of neural networks. The work contains both new original results and generalization of already known ones published earlier in different journals.

Fractional models in hydromechanics

Topic and purpose. The last two decades are marked by wide spreading fractional calculus in theoretical description of the natural processes. Replacement of the integer-order operators by their fractional (and even complex) counterparts opens up a continuous field of new differential equations in which the standard set of equations of theoretical physics (wave, diffusion, etc.) is represented by separate spikelets at points with integer coordinates. But what do the fractional-order derivatives mean physically?

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