Analysis of bifurcations in double-mode approximation for Kuramoto — Tsuzuki system

The article discusses emergence of chaotic attractors in the system of three ordinary differential equations arising in the theory of reaction–diffusion models. We studied the dynamics of the corresponding one- and two-dimensional maps and Lyapunov exponents of such attractors. We have shown that chaos is emerging in an unconventional pattern with chaotic regimes emerging and disappearing repeatedly. We had already studied this unconventional pattern for one-dimensional maps with a sharp apex and a quadratic minimum. We applied numerical analysis to study characteristic properties of the system, such as bistability and hyperbolicity zones, crisis of chaotic attractors.