Occurrence of Chenciner Bifurcation in Two Simple Economic Models with Heterogeneous Expectations

This chapter explores the role of the Chenciner bifurcation in two simple nonlinear economic models with heterogeneous expectations. Through analytical methods and numerical simulations, we examine how this degenerate NeimarkSacker bifurcation leads to the coexistence of multiple attractors, generating complex and path-dependent economic dynamics. By analyzing a behavioral macroeconomic model of inflation and an asset pricing model with evolutionary learning, we show that the Chenciner bifurcation provides a theoretical explanation for persistent volatility, cyclical fluctuations, and instability in financial and macroeconomic systems. Our findings highlight the critical influence of expectation formation and trend-following behavior in shaping market dynamics.