The objective of the paper is to provide a rationale for mathematical models that describe a response to innovations (response to innovations) across industrialised regions of Russia. The paper gives an advanced analysis of trends in a development of industrialised regions. Based on the mentioned analysis, the authors have put forward and tested a number of hypotheses. There are the hypothesis for an unbalanced economic development in industrialised regions of various types, the hypothesis for development distinction, inherent to industrialised regions of certain types, the hypothesis for a catalytic role of the government in the innovation dynamics and the hypothesis for the available response to innovations in the economic system. The authors have proposed a methodology for the response to innovations, proved conditions, under which the response appears in the economic system, grounded types of the response to innovations. The authors have also presented mathematical formalization for mechanism for the response to innovations in the regional production system. In an action-oriented section of this paper, the authors have explored the response to innovations in industrialised regions of Russia. The findings given in the paper can be used to justify mechanisms of the regional industrial policy, as well as evaluate a regulatory impact of valid regulatory legal acts.