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KIAM Preprint ¹ 67, Moscow, 2013
Authors: Malinetskii G. G., Faller D.S.
Transition to chaos in the two-mode system for «reaction-diffusion» models
Abstract:
The article discusses the emergence of chaotic attractors in the system of three ordinary differential equations arising in the theory of «reaction-diffusion» models. The dynamics of the corresponding one- and two-dimensional maps and Lyapunov exponents of such attractors are studied. It is shown that the transition to chaos is in accordance with a non-traditional scenario of repeated birth and disappearance of chaotic regimes, which had previously been studied for one-dimensional maps with a sharp apex and a quadratic minimum. Some characteristic features of the system – zones of bistability and hyperbolicity, the crisis of chaotic attractors – are studied by means of numerical analysis.
Keywords:
nonlinear dynamics, two-mode system, «reaction-diffusion» models, bifurcation, self-similarity, «cascade cascades», attractor crisis, ergodicity, bistability
Publication language: russian, pages: 36
Research direction:
Mathematical modelling in actual problems of science and technics
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