Dynamic analysis of a Solow–Swan model with capital-induced labor migration

Abstract

The Solow–Swan model, introduced in 1956, is a fundamental framework in macroeconomic theory that models long-term economic growth through capital accumulation and labor force dynamics. This research builds on the original Solow–Swan model by incorporating capital-induced labor migration, which is a significant extension considering modern economic contexts where migration plays a crucial role in regional and national economic dynamics. First, we analyze the existence of the solution of the model. Then, we explore the local asymptotic stability and Turing bifurcation of the positive equilibrium. We then study the nonconstant steady state solution of the model as a branch of solution bifurcation from stationary system. And then we investigate the stability of the nonconstant steady state solution. Finally, we present some numerical simulations to verify our theoretical predictions.