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By developing a continuous-time heterogeneous agent financial market model of multi-assets traded by fundamental and momentum investors, we provide a potential mechanism for generating time-varying dominance between fundamental and non-fundamental in financial markets. We show that investment constraints lead to the coexistence of a locally stable fundamental steady state and a locally stable limit cycle around the fundamental, characterized by a Bautin bifurcation. This provides a mechanism for market prices to switch stochastically between the two persistent but very different market states, leading to the coexistence and time-varying dominance of seemingly controversial efficient market and price momentum over different time periods. The model also generates other financial market stylized facts, such as spillover effects in both momentum and volatility, market booms, crashes, and correlation reduction due to cross-sectional momentum trading. Empirical evidence based on the U.S. market supports the main findings. The mechanism developed in this paper can be used to characterize time-varying economic dominance in economics and finance in general. [ABSTRACT FROM AUTHOR]