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Concepts of class struggle and social reproduction are used to explain the sudden collapse of Soviet Communism. I explore these ideas by means of the mathematical theory of dynamical systems. Theoretical focus is upon the power of social classes and how this power changes over time. The Soviet bureaucracy gradually divided into two classes, and the power relations between these ruling classes caused a drastic loss of power by both, which is why the Communist system collapsed. Four classes of Soviet society are considered: political class, administrative class, working class, and capitalist class. I examine the reproduction of class power in two-, three-, and four-class systems. Also analyzed are the effects of random perturbations and the particular impact of the August 1991 coup attempt. Wherever possible, graphs are used instead of equations to explain class dynamics. The results indicate that drastic power loss was not the only possible outcome of Soviet class dynamics, which may be why the collapse was so surprising. The class dynamics approach emphasizes multiple historical possibilities and cuts against any rigid class determinism. [ABSTRACT FROM AUTHOR]