Transition to chaos in the «reaction-diffusion» systems. The simplest 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» systems. 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 been previously 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
• «reaction–diffusion» systems
• bifurcation
• self-similarity
• «cascade of cascades»
• attractor crisis
• ergodicity
• bistability