Equidistant Economy

This chapter elucidates the bifurcation mechanism of an equidistant economy through the analysis of the symmetric group \(\mathrm {S}_N\) . Preexisting results for the direct bifurcation are combined with the rules for secondary and further bifurcations. Invariant patterns in the replicator dynamics in the equidistant economy are obtained. The mechanism of breaking and sustaining bifurcations from these patterns is elucidated. Sustaining bifurcations are unique features of the replicator dynamics. The stability of bifurcating branches is analyzed, demonstrating that most of them are unstable immediately after bifurcation. Numerical analysis of economic geography models demonstrates that direct bifurcating curves connect the curves of invariant patterns, thereby creating a mesh-like network. This network grows rapidly as the size N of \(\mathrm {S}_N\) increases. Chapter 9 is a prerequisite for sustaining bifurcations. This chapter is a foundation of the global system in Chap. 11 .