LAUSR

In the work, a nonlinear reaction-diffusion model in a class of delayed differential equations on the hexagonal lattice is considered. The system includes a spatial operator of diffusion between hexagonal pixels. The main results deal with the qualitative investigation of the model. The conditions of global asymptotic stability, which are based on the Lyapunov function construction, are obtained. An estimate of the upper bound of time delay, which enables stability, is presented. The numerical study is executed with the help of the bifurcation diagram, phase trajectories, and hexagonal tile portraits. It shows the changes in qualitative behavior with respect to the growth of time delay; namely, starting from the stable focus at small delay values, then through Hopf bifurcation to limit cycles, and finally, through period doublings to deterministic chaos.