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We introduce a two-country New Economic Geography model with four regions. lt is defined by a 20 piecewise smooth map that depends on 8 parameters. Using reductions of this map to 10 maps defined on invariant straight lines, we obtain stability conditions of the Core-Periphery fixed points, and show how such reductions can be used to describe basins of attraction of coexisting attractors. Typical bifurcation sequences obtained when varying some parameters are discussed. We find patterns that are much richer than those observed in standard NEG models: there are more types of fixed points including fixed points attracting in Milnor's sense; their basins of attraction are quite complicated; and coexistence is pervasive.
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