This manuscript provides a very interesting and innovative set of stylized modeling experiments to explore the stability of governance structures in environmental systems. The evaluation of system stability across thousands of governance structures using a generalized dynamic systems modeling approach is particularly novel and insightful. The manuscript is well written and organized. I'd suggest the authors address the following comments to further improve the manuscript:

1. The modeling approach necessarily deals with a stylized, abstracted representation of environmental governance systems. While there is some attempt to draw analogies between the mathematical abstraction and real-world systems in the introductory text, such analogies are largely excluded from the description of the model itself, the results, and the discussion/conclusion. I think the manuscript could be improved by providing examples of tangible aspects of real-world systems that the mathematical abstractions might represent (or using a single example, e.g., groundwater systems, and carrying it through the entire manuscript to aid readers with interpretability and bring the modeling formulation to life a bit more)

2. I'm not seeing where "stability" is clearly defined, both conceptually and mathematically. Perhaps I missed it. Regardless, a concise definition of the concept should be up front and center given the manuscript's focus.

3. While the effort to deploy thousands of structural variants of the environmental system is impressive and laudable, it seems to me that the revealed system dynamics still may be subject to higher-level structural assumptions regarding the nature of actor interactions. For example, NGOs are not directly tied to the state of the resource, whereas one might argue that NGOs are inversely (loss term rather than gain term) related to resource state (e.g., the tendency for environmental NGOs to emerge/grow as a particular environmental resource degrades). Likewise, actors could be viewed as operating within a nested structure (e.g., individual resource users interested in preservation of a resource comprising an NGO). While I understand that such a stylized formulation cannot touch upon all of these elements, I think the advantages/disadvantages of the proposed formulation can be further interrogated in the discussion.

4. Given the modeling interest on actors' ability to influence policies or capacities of other actors, there might be some interesting and relevant connections with the power relations and sustainability transitions literature (see for example Avelino and Wittmayer, 2016). Perhaps this could be further explored in the introduction and/or discussion/conslusion.

5. The assumption of a Nash-equilibrium in actors' allocation of efforts is a strong one and receives very limited treatment in the manuscript. While I understand the adoption of the approach from a computational and conceptual standpoint, I think further elucidation of the implications and limitations of such an approach is warranted.

6. The abstract mentions a system's ability to "adapt to social and environmental change" and recover from "perturbations". Can the authors speak more to how perturbations of the system (in the form of either short-term shocks or gradual stressors factors) relates to the formulation? What exactly are the "perturbations in the variables controlled by the governance system" in this particular setup? And how does the concept of stability connect? I think a clearer defintion of stability (see comment above) and some added discussion could bring clarity to this.

Minor editorial comments:

Figure 1 - mismatch between F2,1,1 in the legend and F2,1,2 on the figure

Line 126 - "non-government" to "Non-government"

Line 138 - "them These" to "them. These..."

Figure 2 - Add "small system" and "large system" labels to the graphs (not just the captions) for readability

This manuscript is a very welcome interdisciplinary contribution to Earth System Dynamics at both methodological and applied levels. Methodologically, it brings out solid dynamical systems approaches to addressing the highly nontrivial problem of environmental governance, where natural and human processes and interactions come into play that require not only the traditional dynamical systems principles in a sterile manner, but also social systems thinking with active decision making rather than the classical determinism. In this regard, this is a very insightful contribution that finds good grounds in an emerging but already reliable literature at the interface between natural and social systems with robust analytical mechanics principles and metrics (and dynamical systems in particular).

The stylised nature of the mathematical conceptualisations and experiments is crucial to shed light onto key interactions, with neither aiming at too much detail, nor at a too-macro of a picture that would wash out critical nonlinearities. As such, this is a very well balanced study, obviously with the inherent limitations that come with such exercise. The authors have done a pretty good job in laying down their reasoning so that it is clearly understood where things come from and what they are meant to represent.

However, it is important to further clarify to those readership that is perhaps not so familar with one of either dynamical systems or governance reasoning the key notions being applied since aspects such as stability per se mean different things to different scientific communities. Further mathematical detail, while often discouraged in other venues, is never too much in this study, hence the authors are encouraged to add, perhaps in annex not to break the pleasant and clear flow of the text, further details on the underlying mathematical physics principles supporting their formal reasoning and formulation.

The conditions under which their formulations are applicable and not should also be further discussed with additional few sentences so that the more naive reader is not tempted to throw the models around without enough care. The authors were clearly careful and that is very well seen through the solidity of their argumentation, formulation, results and discussion. But an additional pedagogic little touch would be the cherry on top of the cake to further help the increasinly mathematically fragile geoscience readership and even more so those coming from the more social science side that might alsot be interested.

Last but not least, the remarks raised by the other referee are also hereby endorsed and will not be repeated. I would not say better in such regards.

All in all, this manuscript is definitely suitable for publication at Earth System Dynamics, is mostly appropriate at the scientific and technical levels safe for the minor aspects raised by both of us, and would also benefit from providing an extra layer of clarification and caution so that a broader readership other than us more technically minded can actually appreciate better the value and harness the vast potential of this contribution.

Thank you and all the best.