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The study of the functioning of hepatitis B viruses in liver cells using methods of mathematical modeling is considered one of today's pressing issues. In this article, the domains of functional-differential equations in a mathematical model of regulatory mechanisms of hepatocytes interacting with hepatitis B viruses (HBV) are presented. Characteristic molecular genetic systems regulatory mechanisms of the interrelated activities of liver cells and HBV are analyzed. A series of computational experiments show that the "chaos" and "black hole" theories describe two of the more dangerous regimes. As a result of the analysis of the "chaos" regime, small regions with normal behavior, "r-windows" were revealed. These regions allow the system to move from a "chaos" regime to a "regular" or normal regime. The features of the area of the regulatory activities of molecular genetic mechanisms of hepatocytes and HBV under a chaotic regime were characterized by analyzing the dynamics of the Lyapunov exponent. Small regions with regular behavior, "r-windows" in the field of dynamic chaos were defined. The regulatory nature of hepatocytes and HBV can be moved from the region of dynamic chaos to the normal region by using "r-windows". The results of a computational experiment quantitatively analyzing the regulatory mechanisms of liver cells and HBV are presented. [ABSTRACT FROM AUTHOR]