Transition to chaos in the two-mode system for “reaction-diffusion” models

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.