Extended Solow–Swan model for capital and natural resources with the Allee effect

Abstract

We study an extended Solow–Swan model for capital, denoted by K, and natural resources, denoted by N . We are interested in production, denoted by Y , expressed by a simplification of the Cobb–Douglas function Y = f(K,L,A) with L = A = 1. We study the model described by the following system of ODEs: { K̇ = sKα − δK, Ṅ = rN ( N CT − 1 ) ( 1− N CC ) − γ0K. We study the asymptotics of solutions; among other things, we find critical points, determine their stability and find their attraction basins. This article was inspired by [M. Kornafel, I. Telega, Int. J. Sustainable Economy 12 (2020), 1–24].