Racetrack Economy: Hierarchical Bifurcation and Invariant Patterns

The mechanism of the direct bifurcation from the uniform state in the racetrack economy was presented in Chap. 3 . This chapter extends this mechanism to a broader context. First, we obtain invariant patterns that are solutions to the governing equation for any value of the bifurcation parameter. Among the plethora of theoretically possible invariant patterns, we identify those that become stable within economic geography models. Next, we introduce sustaining bifurcation, which is a unique bifurcation in the replicator dynamics. Last, we describe the hierarchical bifurcation from the uniform state. A likely course predicted for \(2^k\) places is a gradual and successive process, called a spatial period-doubling cascade. This chapter is a prerequisite for sustaining bifurcations in Chaps. 11 and 14 . This chapter provides the theoretical foundation of racetrack economy analogy for a long-narrow economy in Chap. 12 and for a square lattice in Chap. 13 .