This study delves into the intricate dynamics of sustainable fisheries through the lens of mathematical modeling, specifically employing the Lotka-Volterra equations. The Lotka-Volterra equations, originally conceived to understand predator-prey interactions, offer a potent framework to model and predict fish population dynamics within aquatic ecosystems. The aim of this research is to demonstrate the applicability and efficacy of the Lotka-Volterra equations in understanding the delicate balance of fish populations and aiding sustainable fisheries management. Through this mathematical approach, we seek to provide a structured methodology and present results that showcase the potential of this model in predicting and managing fish populations. In our analysis, we adjust the parameters of the Lotka-Volterra equations to simulate various scenarios, enabling a comprehensive understanding of sustainable fishing practices. Our findings underscore the significance of mathematical models, particularly the Lotka-Volterra equations, in informing strategies to maintain fish populations in a sustainable and ecologically balanced manner, thereby ensuring the longevity of marine ecosystems and the fisheries thatrely upon them.

The Energy Return on Energy Invested, EROEI, is known as an important parameter for evaluating the efficiency of energy-producing technologies. In this paper we examine the concept of EROEI from a general viewpoint, giving insights on a wider range of applications. In general, natural resources can be seen as energy stocks characterized by a “potential” that can be exploited by creating intermediate stocks. This transformation is typical of dissipative systems and for the first time we found that Lotka-Volterra model, usually confined to the study of biology of populations, can represent a powerful tool to estimate EROEI for some such systems, providing an understanding of the reason for the overexploitation phenomenon and, in some cases, the collapse of the exploiting system.

The bilateral trade relationship between PRC and ASEAN is close. As early as 2012, China has been the largest trading partner of ASEAN, and ASEAN has also taken the place of the United States as PRC’s second largest trading partner in 2019.This paper uses the theory of ecological population evolution, selects the total import and export volume of PRC and the ten ASEAN countries from 2000 to 2019 as the data sample, studies the bilateral trade relations between PRC and the ten ASEAN countries, analyzes the competition and symbiotic relationship of bilateral trade between PRC and the ten ASEAN countries and the possibility of trade friction according to the results, and proposes corresponding improvement strategies. According to the results of the population evolution competition model, China has a competitive relationship with Indonesia, Malaysia, the Philippines, Singapore and Thailand, which is most likely to cause trade friction. China has a biased relationship with Brunei, Cambodia, Laos, Myanmar and Vietnam, which is more likely to cause trade friction. On this basis, in order to further strengthen the trade relations between PRC and the ten ASEAN countries, this paper puts forward policy suggestions on improving infrastructure, strengthening independent innovation, seeking cooperation fields and actively investing abroad.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.