The authors consider a demo-economic model where the economy consists of two sectors ("hunting and farming" and "industry"), and both sectors depend directly or indirectly on the explanation of a renewable resource. The primary sector harvests a renewable resource (fish, corn, or wood) which is used as the input into industrial production, the secondary sector of our economy. Labor is divided up between these two sectors under the assumption of competitive labor markets. A system of two nonlinear differential equations for the resources and the population is studied by phase space analysis. Using the Hopf bifurcation theorem, the authors obtain two different routes to limit cycles and prove numerically the existence of a stable Malthusian limit cycle.

中文翻译：

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内生人口增长和可再生资源的开发

作者考虑了一个民主经济模型，其中经济由两个部门（“狩猎和农业”和“工业”）组成，并且这两个部门都直接或间接地依赖于对可再生资源的解释。初级部门收获可再生资源（鱼、玉米或木材），用作工业生产的投入，即我们经济的第二部门。在劳动力市场竞争的假设下，劳动力在这两个部门之间分配。通过相空间分析研究了资源和人口的两个非线性微分方程组。使用 Hopf 分岔定理，作者获得了两种不同的极限环路径，并在数值上证明了稳定马尔萨斯极限环的存在。