Stochastic, blow-up, and slow time regimes in wave dynamics under self-organizing or periodic disturbances

The paper considers unlimited modes of blow-up exacerbations, in which phase variables that tend to the Poincare circle are aggravated in a finite time, as well as models of localization modes, in which localization modes and stochastics in the diffusion layer at the equator of the Poincare circle arise along with blow-up modes, not contradicting each other. Sufficient conditions are given for the presence of blow-up modes with exacerbation and conditions for the existence of stochastic modes in some models of autowave and oscillator systems with small periodic perturbations and spatial diffusion.