Investigation of Turing instability for the Gierer–Meinhardt model

The dependence of the emergence of Turing instability for a distributed system of nonlinear differential equations that describe hydra morphogenesis based on the oscillatory properties of the corresponding trajectories of the system was investigated. The limits in the parameter space that provide diffusive instability were obtained. The frequency and amplitude dependences of the resulting spatial self oscillations on the values of the main parameters were investigated. Comparative analysis of the properties of the distributed system and corresponding trajectories of the system was carried out and the analytical conclusions were confirmed by the solutions of the system that were found using MATLAB.