Simulating urban expansion as a nonlinear constrained evolution process: A hybrid logistic–Monte Carlo cellular automata framework

Urban expansion is an inherently complex and nonlinear process shaped by heterogeneous spatial patterns, temporal dynamics, and stochastic uncertainties. To model such complexity, this study presents a novel hybrid framework that integrates logistic function-based urban proportion prediction with an adaptive Monte Carlo simulation under a cellular automata (CA) structure. The logistic function captures the nonlinear, sigmoidal growth trend of urban saturation at a microscale, while the adaptive Monte Carlo introduces controlled randomness based on local growth rates and probabilistic stratification. This dual mechanism enhances the system's capability to simulate emergent urban dynamics governed by local interactions and macro constraints. Empirical validation in Changsha, China, shows that the proposed model achieves over 5 % improvement in F1-score accuracy compared to traditional CA-Markov models. Moreover, it reveals spatially differentiated urban transformation pathways and enables city-scale prediction constrained by dynamically evolving local capacities. The model features emphasized adaptability and transferability. This interdisciplinary approach demonstrates strong potential for understanding and forecasting complex urban systems from a nonlinear and data-driven modelling perspective.