диссипативные структуры

The influence of additive homogeneous isotropic field of Gauss fluctuations of dynamical variables of Gierer–Meinhardt model to formation of dissipative structures in soft mode regime was investigated. The system of equations for description of undamped modes interaction was received. It was shown that fluctuations of dynamical variables are widening the instability region. The numerical simulation of considered model with different boundary condition was performed.

The influence of multiplicative fluctuations of parameters of reaction­diffusion system on example of Gierer–Meinhardt model to formation of dissipative structures in soft mode instability regime was investigated. The system described interaction of non­decreased modes (order parameters) was received. It was shown that fluctuations of parameters are lead to changing of number of unstable modes, shifting of their eigenvalues and parametrical excitation of the system. The numerical simulation of described model evolution was received.

Self­organized structures after ion­beam irradiation in solid materials have been studied using the method of fractal dimension. General computer method of the scale invariance evaluation for exposed dispersive structures is described. It was demonstrated that structures after irradiation can be characterized by the compatibility of scale invariance properties at different scale levels.