A Stochastic Capital-Labour Model with Logistic Growth Function
Houssine Zine, Jaouad Danane, Delfim F. M. Torres
TL;DR
This paper introduces a stochastic capital-labour model incorporating logistic growth, analyzes its solutions, and provides conditions for labour force extinction and persistence, supported by numerical simulations.
Contribution
It presents a novel stochastic model with logistic growth and derives new conditions for labour force extinction and persistence using Lyapunov analysis.
Findings
Unique positive global solution established
Conditions for labour force extinction derived
Numerical simulations validate theoretical results
Abstract
We propose and study a stochastic capital-labour model with logistic growth function. First, we show that the model has a unique positive global solution. Then, using the Lyapunov analysis method, we obtain conditions for the extinction of the total labour force. Furthermore, we also prove sufficient conditions for their persistence in mean. Finally, we illustrate our theoretical results through numerical simulations.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Economic theories and models