In the midst of crisis and growing uncertainty of economic development, it's becoming ever more important to investigate economic cycles and bifurcation states where small regulatory changes can give the dynamic process completely different properties. The research methodology is based upon three principles that enabled the author to develop a new cyclical behavior model and examine the cyclicity factors other than those in the Goodwin cycle model. The inductive approach relies on the universal pattern of the relationship between economic variables and rules out incorporating additional theoretical assumptions. As opposed to the deductive approach, empirical assessment of indicators is determined before the analysis of the model and has a decisive impact on the nature of the conclusions. The principle of reflexivity means that the subjects of a particular market are at the same time objects affected by another one. This principle is implemented in the assumption that demand and supply functions in every market depend both on the price and the change of all prices. The principle of linearity establishes a linear relationship between endogenous variables and their derivatives and allows to examine cyclic processes and bifurcation states by way of a relatively simple system of first-order linear differential equations which includes the conditions of the Keynesian equilibrium and the labor market equilibrium. The paper develops the theoretical and instrumental framework for a reflexive model of economic dynamics, provides analysis thereof for the case of two and three related markets, determines the cyclicity conditions and the characteristics of bifurcation states, and examines the nature of the dynamics of macroeconomic variables. A number of conclusions stem from the study. Firstly, the model has shown its efficiency in analyzing cycles in reflexive markets, with the simplifying assumption that the functions are linear not becoming an obstacle to describing and exploring various types of dynamics and bifurcation states. Secondly, exogenous parameters of the model can be identified empirically prior to its analysis, which allows to address the distinctive features of dynamic processes with an eye on the institutional character of economic systems. Due to the linear nature of the model, it is possible to make calculations using regression analysis methods based on publicly available monitoring data, which increases the practical relevance of the model. Thirdly, the model allows for generalization for an arbitrary number of reflexive markets, an important line of future research being the study of a four-dimensional model with a foreign-exchange market as well as a global model of the world economy with a reflexive relationship between all markets.