Elsevier

Ecological Modelling

Volume 368, 24 January 2018, Pages 69-77
Ecological Modelling

Sustainability factors in dynamical systems modeling: Simulating the non-linear aspects of multiple equilibria

https://doi.org/10.1016/j.ecolmodel.2017.11.008Get rights and content

Abstract

What is sustainability? Sustainability is a concept that can be defined in many ways depending upon a society's perception of current material needs and the actual material needs of future generations. Much of our ability to achieve sustainability entails developing indicators and measurements that will guide us to this goal. This paper suggests that we can strengthen the prediction of sustainability indicators by adopting a “multiple equilibria” approach for a more effective decision-making process in various sectors of the economy, in ecosystem protection, or in political arenas. There is an emerging need for further development of predictive mathematical models of system sustainability over economic growth models for sustainable resource measurement and management. The objective of this paper is to use computer modeling and differential equations to simulate the “multiple equilibria” of a 3 variable real world system. In our study, we tested the theoretical validity of “multiple equilibria” sustainability modeling through simulated measurements of precipitation and nitrogen runoff into a hypothetical lake. As a quantitative tool to model, the “multiple equilibria” techniques can have tremendous predictive power for business leaders, political decision makers, and environmental scientists, and assist in better management of ecological, economic, and material resources in short-term and long-term end-use scenarios.

Section snippets

Introduction: why sustainability is important

Biophysical sustainability is the process of balancing resource stocks and flows within a dynamical system over time. Sustainability is a universal necessity, because, in the natural world, an ecosystem thrives on the symbiotic interaction of numerous individual organisms and communities of organisms that depend on each other biologically and ecologically. Thus, an ecosystem dynamically strives to be in equilibrium but often finds itself far from equilibrium in real world scenarios. But a

The Limits to Growth model

Early research on sustainability used the predictive power of computer modeling to simulate how dynamical systems would behave, and eventually brought attention to the stress on natural resources by growing human populations and the limited carrying capacity of the Earth's ecosystems. In the late 1950s, MIT Professor Jay Forrester established the field of “systems dynamics” by using mathematical modeling to analyze the behavior of complex engineering and social systems. Forrester's computer

The theory of multiple equilibria

According to Shackley (2000), “[In] a system with many interacting variables and feedbacks, the relative significance of which cannot be assessed a priori, many of which may realistically change on the time and space scales of interest, and which are heterogeneous in the sense that they include a wide range of natural and social processes, computer or simulation modeling sometimes seems the only viable research strategy.” This assumption was apparent when we contemplated the approach to be

Modeling multiple equilibria

As a quantitative tool, the goal of modeling the “multiple equilibria” technique is to provide predictive power for business leaders, political decision makers, and environmental scientists, and assist in better management of ecological, economic, and material resources in short-term and long-term sustainability scenarios (Jiang and Shi, 1995). In this section, we use computer modeling to simulate “dynamical systems” of a three (3) variable real world system. We make explicit the simulation of

Future research

As with the Limits to Growth model, our goal is to simulate possible, as well as, probable realities. The Club of Rome employed statistical data to model future scenarios based on past information and projecting those patterns into “standard runs”. These runs, in turn, could be used to simulate different trajectories by manipulating the data. While some trajectories were more optimistic than the original standard run, all future scenarios suggested inevitable resource exhaustion due to

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