(682e) Sustainability Identification for N-Dimensional Systems

Masih Jorat

Dept. of Chemical and Biomolecular Engineering, UCLA, Los Angeles, CA, 90095

Vasilios I. Manousiouthakis

Dept. of Chemical and Biomolecular Engineering, UCLA, Los Angeles, CA, 90095

The severity of degradation of the natural environment and look for a comprehensive solution in the form of flexible and multisided assessment tool analyzing the human impacts on its surrounding environment has led to the introduction of the concept of sustainability, to assist global, national and local policy making organizations, research institutes, and citizens at large, in assessing the current state of their environment and in developing solutions for its improvement. The development of sustainable strategies cannot be pursued in an efficient manner, without a comprehensive, rigorous, and unbiased definition of sustainability. Through utilizing the concept of positive invariant sets, the novel concept of Sustainability Over Sets (SOS) [1] provides a conceptual framework within which the time evolution of a system can be analyzed. SOS formalizes the incorporation of human input into the sustainability assessment process, first by defining a set in state-space which exactly quantifies human input regarding what is sustainable, and by then modifying the question “is a system sustainable?” to “is a system sustainable over a predefined set?” which is amenable to definitive (yes or no) answers. A system is sustainable over a set (SOS) in the system’s state-space, if the system’s state trajectories initiated within the set, remain for all time within the set, in other words the system’s vector field is directing inwards at the set's boundaries. In this work we present computational algorithms that can identify sustainable regions in the state-space for n-dimensional systems which are not easily visualized due to their high (more than three) dimensions. This evolution of the SOS concept can respond to cases, in which sustainability restrictions are expressed in terms of multi variable functions. For example, Food webs are a central, if not the central, idea in ecology. A food web graphically represents the paths of nutrients and energy through the living components of an ecosystem and the context in which individuals exploit their prey and avoid their enemies.To demonstrate the practical applicability of the algorithm to be presented, it identifies the sustainable sets of a ten-dimensional food web, with nine different species and a nutrient pool [2].

[1] Manousiouthakis VI, Jorat M. Sustainability over sets. Environmental Progress & Sustainable Energy. 2017 Oct

[2] Fath BD, Cabezas H, Pawlowski CW. Regime changes in ecological systems: an information theory approach. Journal of theoretical biology. 2003 Jun 21;222(4):517-30.