Electron. J. Differential Equations, Vol. 2023 (2023), No. 59, pp. 1-22.

Analysis and simulations of the HANDY model with social mobility, renewables and nonrenewables

Meir Shillor, Thanaa Ali Kadhim

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,
DOI: 10.58997/ejde.2023.59

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Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: shillor@oakland.edu
  Thanaa Ali Kadhim
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: taalkhawaja@oakland.edu

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