**5. Conclusions**

The various teams working on SPT have been exploring SPT research as a candidate for a General Systems Theory (GST) and for systems science, both of which need a means for testing abstract models. This research answered the question, "How do you test abstract models of systems?" By modeling the Cycles ISP using MP, we were able to test and reason about cycles in a new and formal way, using automated tools to unravel and expose the inherent patterns within cycles occurring both alone and in groups. This paper thus established productive applicability of MP software to the SPT problem space, in which MP event traces could comprise a library of mini-models envisioned for each ISP.

Earlier discussions about cycles and other ISPs were based on natural language descriptions and informal models at best. None of the discussions were supported with formal models of behavior like the cycle model contained herein. MP was tried as a tool for generating mini-models of systems mechanisms that are general and discipline-independent. Cycle behavior was described as a set of step-by-step procedures—an algorithm—that was executable in computer space to see many possible instances and variants of cycles. These mini-models of cycle instances did generate additional information about cycles that had not been obtained to date by comparison of the real systems counterparts to the modeled mechanism (specifically, illustrating the connection of positive and negative reinforcements to cycles). It also demonstrated that many of the known cycle variants arise from a single compact formal specification of cycle behavior. The MP model of just one ISP was a source of new knowledge about the mechanism for that individual ISP, showing that MP is a productive framework for describing the Cycles ISP as a formal and executable model, in terms of a simple and straightforward event grammar.

The abstract Cycles ISP MP model shown in Figure 6 was tested in four different domains by adapting the event name language as shown in Table 1. The MP simulation results of each model "unraveled" specific instances of cycles that fit the patterns previously considered distinct ISPs. In Figure 5, we have evidence from the MP simulation runs that some ISPs previously considered as separate from cycles are in fact special cases of cycles. Figure 8 shows the oscillation pattern emerging from each of the four domain-specific cycle models tested, demonstrating the isomorphic nature of the Cycles ISP. MP provides automation to facilitate the study of how ISPs are related, and opens the door to future work in this area.

## **6. Future Work**

Since the use of MP achieved both extension of our knowledge base of cycles and cycling and at the same time provided the means to test that knowledge base, we consider it a promising potential source of significant advancements in both general theories and specific applications. Future work will apply instances of the Cycles ISP in several different domains to generate more concrete examples of where these patterns occur, and which deviations might result in system dysfunctions or pathologies. MP will be used as an experimental framework for collecting synthetic data about modeled ISPs for comparison to empirical data collected from real world systems, opening a new avenue for hypothesis testing for SPT. Knowledge gained through the use of automated modeling tools like MP might contribute to knowledge of why deviations from expectation occur at the fundamental general systems level, what exact impacts they have, and how they might be corrected, especially when modeled in the context of interactions with other systems. Producing more models of many ISPs would allow placing the abstracted model in computer space for artificial systems research [7]. Additional steps would then be taken to integrate other proposed ISPs into an overall SPT-MP meta-model, creating more exploratory executions of ISP behaviors and eventually of ISP interactions, and cataloging the formal

MP models of ISPs. The ultimate goal would be to interconnect a sufficient number of the ISPs to yield a very general model of sustainable systems dynamics at all scales and for many types or classes of systems as well as models of dysfunction that are often encountered in engineering and natural systems.

Another fascinating challenge would be to encode the SPT Linkage Propositions (LPs) that describe behavioral influences of one ISP on any other or between many ISPs [49]. This activity would be expected to challenge and yield strong benefits or expansions of understanding of both SPT and MP. For example, how could one encode LPs (perhaps the most creative and original contribution of SPT) in MP models, given that it itself explores behavioral alternatives? How would MP handle hundreds of LPs? Would such MP SPT systems models then more adequately approach or explore such conundrums as "complexity" and "emergence" which are of grea<sup>t</sup> interest to both systems engineers and systems scientists?

Beyond the LP extension of individual ISP MP models, future work could include using MP to explore another line of research spun off from SPT, namely, Systems Pathology. MP has already demonstrated its ability to expose the negative aspects of a process, i.e., how systems don't work or dysfunction [27,39]. Once the alternative behaviors of an ISP are modeled, MP could be used to eliminate some of the behaviors, constraints, or LPs and assess how this changed or caused dysfunction in the normal operation of an ISP in various and changing environments and contexts.

MP provides a virtual systems laboratory for reasoning about the behaviors of systems based on a series of events that unfold given the presence or absence of linkages or dependencies. MP may be used in the future to support or refute various claims made about cycles and other ISPs, leveraging the formality it brings to the description of ISPs and their various manifestations.

**Author Contributions:** K.G. wrote the MP models, performed the experiments, and contributed the descriptions of the MP framework to the paper. L.T. provided the source data for the models, contributed the descriptions of the SPT, and documented the implications. Both K.G. and L.T. wrote the Introduction, Conclusions, and Future Work.

**Conflicts of Interest:** The authors declare no conflicts of interest. No sponsor had a role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
