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


Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.

Nonlinear two-dimensional dynamics of interacting cancer cells under extracellular field conditions

Purpose of this work is to theoretically investigate the effect of extracellular field on antiparallel and parallel transfer of interacting cancer cells depending on external parameters of extracellular matrix and parameters of metabolic potential profile in the dynamics of cancer tumor formation and development risks. Methods.

Modeling of gradient-like flows on n-sphere

A general idea of the qualitative study of dynamical systems, going back to the works by A. Andronov, E. Leontovich, A. Mayer, is a possibility to describe dynamics of a system using combinatorial invariants. So M. Peixoto proved that the structurally stable flows on surfaces are uniquely determined, up to topological equivalence, by the isomorphic class of a directed graph. Multidimensional structurally stable flows does not allow entering their classification into the framework of a general combinatorial invariant.

Self-oscillating system generating rough hyperbolic chaos

Topic and aim. The aim of the work is design of rough chaos generator, whose attractor implements dynamics close to Anosov flow on a manifold of negative curvature, as well as constructing and analyzing mathematical model, and
conducting circuit simulation of the dynamics using the Multisim software.

Investigated models. A mathematical model is considered that is a set of ordinary differential equations of the ninth order with algebraic nonlinearity, and a circuit representing the chaos generator is designed.

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