Review of Actual Problems of Nonlinear Dynamics

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.

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.

Topic and aim. The aim of the work is to review circuits of chaos generators, those described in the literature and some original ones, in a unified style basing on circuit simulations with the NI Multisim package, which makes the comparison of the various devices apparent.

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.

We consider important problems of modern theory of dynamical chaos and its applications. At present, it is customary to assume that in the finite-dimensional smooth dynamical systems three fundamentally different forms of chaos can be observed.