Mathematical modelling of the contrast dissipative structures in the field of fluctuations of dynamical variables

The influence of additive homogeneous isotropic field of Gauss fluctuations of dynamical variables of Gierer–Meinhardt model on the formation of dissipative structures in the soft mode of their excitation was investigated. The system of equations for the description of undamped modes interaction was received. It was shown that fluctuations of dynamic variables widen the instability region. The numerical modelling of evolution of the considered model with different boundary conditions was performed. It was shown that rising of random component of parameters of dynamical variables lead to acceleration of destruction of homogeneous stationary state and forming of dissipative structures far from Turing bifurcation and to its deceleration nearby this bifurcation. The estimation of times of transitions of the system was performed using the calculation norm of matrix of difference of concentration of reagents.