Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 59, pp. 1-22.

Title: Analysis and simulations of the HANDY model with social mobility, renewables and nonrenewables
       
Authors: Meir Shillor (Oakland Univ., Rochester, MI, USA)
         Thanaa Ali Kadhim (Oakland Univ., Rochester, MI, USA)
         
Abstract: 
We expand the HANDY (Human And Nature DYnamics) model for the socioeconomic
dynamics of a large stratified society. The basic  model was introduced in
Motesharrei (Dissertation 2014) and Motesharrei et al. (2016).
It is a nonlinear system of ODEs for a `simple society' of  Elites,
Workers, Wealth, and Natural Resources. Following  Ali Kadhim (Dissertation 2021),
we add social mobility between the classes and split  natural resources into
renewables and nonrenewables.  We establish  the existence, boundedness and
positivity of the solutions, and investigate the stability of the steady states.
The model admits stable steady states, and there is numerical evidence of stable
periodic solutions and limit cycles. Simulations depict the different
qualitative types of model behavior: convergence to steady states, periodic
oscillations or collapse.

Submitted January 17, 2023. Published September 15, 2023.
Math Subject Classifications: 91D10, 37N99, 34C60.
Key Words: HANDY model; social mobility' renewables and nonrenewables;
 socioeconomic dynamical system; ODEs analysis.