This paper develops a spatial agent-based model to examine how fertility regime shifts reshape population concentration and wealth distribution in an abstract urban system. Migration decisions combine population preference, cultural homophily, expected net income, and resource endowment through a standardised softmax utility. The design is deliberately stylised: it is not calibrated to a particular country or city system, but is intended to isolate the feedbacks linking migration, fertility, urban scaling, and accumulated wealth.
The simulations reveal robust directional asymmetry. When fertility shifts from low to high, population concentration responds rapidly; when fertility shifts from high to low, concentration declines only after a detectable delay and may temporarily continue in the previous direction. Wealth adds a second layer of hysteresis: cell total-wealth concentration follows population concentration with delay, cell mean-wealth inequality and system-level wealth indicators are slower still, and phase-space trajectories form loops rather than collapsing onto a single population–wealth curve. Robustness experiments indicate that longer fertility cycles, wider mobility neighbourhoods, and smoother resource landscapes change the magnitude of delay and overshoot, but do not remove the qualitative asymmetry. The paper argues that demographic decline should be understood not as the mirror image of demographic expansion, but as a path-dependent transition mediated by fast migration-income feedbacks and slower fertility, cohort, culture, and wealth mechanisms.