I have read the paper with pleasure. It flows well, the language is very careful. It is also a nice short course into paleoclimate, with many useful references.

I wonder actually who first-authored the paper. If Prof Ghil “conceived and designed the study”, why would he not write the paper? Or, if he did, why is he not the first author?

Beside the purpose of reviewing past efforts, I appreciate the intention of pointing to new directions, and anticipating soon-to-be-reported new results.

I do sympathise with Dr Daruka Istvan (whom i don’t know) if he has misgivings about any misrepresentation of his work, even if inadvertantly, especially regarding novelty. Although i should say that being completely ignored would be worse. I would like to kindly request from the authors that they do their utmost to be fair. Probably i didn’t even need to say this any more.

Some specific points follow below. More details on these can be found in the attached annotated manuscript.

1. The term “interaction” is used in this paper as often as we encounter it in general. However, i don’t really understand what is meant by this so often, including in this paper. Please clarify, or, if it is not possible, avoid using this language. As i understand, interaction is about two-way causality, which only makes sense in terms of couplings in governing equations.

2. I also don’t understand the paper’s distinction between stochastic and deterministically chaotic sources of (internal) variability.

3. In contrast, i think we should distinguish between external forcings versus influences under internal variability. Stochastic terms in equations are not meant to represent external forcing.

4. Point (ii) in the definition of a pullback attractor might be redundant. This might be the correct conclusion to be drawn from Fig. 11. The situation might be parallel with a time-dependent version of the system that is the normal form for a pitchfork bifurcation. I suppose that the PBA of that system — that goes back to negative infinity in time — is a pullback fixed point that is associated with the single stable solution and unstable solution before and after the bifurcation point, respectively. I suppose that after the bifurcation, we have PBAs that do not go back to negative infinity. This should have serious implications for climate projections.

Please see details and other minor comments and questions in the attached annotated manuscript. I hope it will be helpful.

Note: I always review non-anonymously, and never make recommendation for or against publication. The recommendation that i make is only to circumvent the rigidity of the submission system, and therefore please consider it void. 

Tamas Bodai

My expertise is in deterministic dynamical systems, so I will focus my comments on that aspect of the paper.

This is a useful paper which summarises paleoclimate research and shows how a nonautonomous dynamical 

systems approach could be useful. I like that the paper has many examples and is easy to read.

Nevertheless, there are a few areas for improvements.

More significant:

   1. It is not clear to me what level of mathematical knowledge this paper is targeting. The paper 

    begins assuming very little knowledge, by examining Hopf Bifurcations in equations (3--5) which are a topic covered

    in any dynamical systems course. Yet later in the paper readers are assumed to know what the 

    `Hausdorff semi-distance' is. I think it would be better to assume less mathematical knowledge than more,

    perhaps the Hausdorff semi-distance could be replaced by a more informal comment about the system 

    approaching $\mathcal{A}_t$. Another place the analysis could be streamlined without loss of

    understanding is by setting $\beta = \mu/2$ in equation (17) thereby reducing the number of parameters.

    The paragraph starting on line 304 provides conclusions without justification, which are only obvious

    to people familiar with dynamical systems. Perhaps a figure would help here?

    

    2. The point of this paper is to demonstrate the advantage of the NDS picture over the autonomous

    picture, yet much of the analysis could be done in the autonomous regime using standard assumptions

    about timescale separation. In the analysis of the FHM model, $\gamma$ is taken to be a slow 

    oscillation which allows for a discussion (lines approximately 385--400) that would be 

    familiar to people who had only worked with autonomous systems. In the Daruka-Ditlevsen model, $\alpha$

    and $\beta$ are again slow parameters, so why shouldn't this be analysed with the classic tools

    of autonomous dynamical systems? I think it would be useful to emphasise what extra information the 

    nonautonomous picture gives us, and what would go wrong analysing it using the tools from 

    autonomous dynamical systems.

    

    3. I find the section on RDS a bit disconnected from the rest of the paper. There are no 

    concrete paleoclimate applications given and the section introduces concepts such as the Random Attractor which is

    not defined even informally and are not used in the rest of the paper. I would recommend either cutting 

    this section or adding in a simple paleoclimate example.

    

    4. Figures 8 and 9 are seriously misprinted, e.g. Fig 8e has times labelled as

    -20000,-000,-0000,-000,0,000,0000. 

     

     I realise this is a matter of personal preference, but might the PBA figures  e.g. 5a look clearer 

     if projected onto the x-y plane? I always find 3D figures confusing. 

     

     Figure 5c doesn't seem useful, perhaps it could 

     be replaced by the trajectories of the system with different $\omega/\nu$ values. 

Little things:

    1. Lines 31--32 `an the' should be `and'.

    2. Around lines 455, what do the parameters mean physically?

    3. Lines 518--527, why not quote Emiliani and Geiss directly?

The paper is generally well written and will be a valuable resource for references on specific ideas related to simple models used for understanding the climate variability in the Earth System from the millennial time scale to the million year time scale during Pleistocene ice age cycles. Also the paper brings the reader up to speed on recent theory on autonomous, non-autonomous and random dynamical systems. I like how the authors use very simple systems to illustrate the pertinent  dynamical systems and attempt to illustrate the pullback approach and pullback attractor with selectively chosen simple models. While I don’t consider there to be any significant advancement in our understanding of millennial scale climate variability or the Mid-Pleistocene transition, there are some incremental improvements over the previous literature in that the proposed lower-order dynamics are illustrated very elegantly. I really only have some minor comments that should be relatively easy to address. 

Comments and typos:

At lines 102 (section 1) the authors bring in the notion of a Hopf bifurcation with one type of simple system (eqn 5). Then in section 2.2 the description of the subcritical and supercritical Hopf bifurcations are described with another system (eqn 6).  I would like to see more diagrams in Section 2.2 (some of us can visualise in our head what is happening when parameters are varied (e.g. through a Hopf bifurcation) but I think it is important to try to improve section 2.1 and 2.2 in a more unified way so at make these sections more accessible to a newer audience that is reading this type of material for the first time. I think a clear illustration with both language and an additional set of figures (possibly using the example systems from equation 5 or 6)  would be helpful. For example, one might introduce the sections with  language such as, “A Hopf bifurcation occurs when a periodic solution or limit cycle that surrounds an equilibrium point appears or disappears when a (control) parameter is varied. When the stable limit cycle surrounds an unstable equilibrium point, the bifurcation is supercritical. In the case that the limit cycle is unstable and surrounds a stable equilibrium point, the bifurcation is subcritical.”  And then also illustrated these concepts later on with the simple systems used.

In general the paragraphs are quite short (e.g Line 54). There is no need to start a new paragraph in a lot of places in the manuscript, please try to make the text flow a bit better.

L243, 249 monotonic, monotonically

I like the section on the pullback attractor and the figures used for illustration of the concepts in this section and therefore this section is a useful resource for general audiences. 

In the section on 3.3 on applications D-O events.

Figure 8a is a bit confusing , maybe I missed it , but I don’t see how the abscissa and ordinate are defined , it looks like simply x and y, yet they are both scaled to \alpha? For example at line 371, the description of the  gamma and the fixed points that arise. I don’t see any description on how the y = \gamma nullcline intersecting the cubic polynomial P_3(x,y) (manifold)  is what determines the unstable or stable fixed points of the system. There are a lot of \alpha symbols illustrated on Figure 8a but there is no clear description in my opinion. 

In FIgure 8c the authors show the non-autonomous forcing for \alpha(t) and then on line 378 they introduce the non-autonomous \gamma and it is not clear what physical implications that \alpha provides although \gamma is related to CO2 eventually, and how the two non-autonomous forcing are related. The authors have not referenced or discussed how this work relates to or improves upon the work of Roberts and Saha (2016) which also illustrate non-autonomous dynamics on a FHN type model. In particular Roberts and Saha draw particular attention to how they modulate the slow manifold through time dependent changes and attempt to relate it to physical mechanisms (e.g. insolation forcing). They also introduce the time dependent sinusoidal forcing on the linear nullcline in the slow component of the slow-fast system. I’m not sure which processes are more important in attempting to explain the last glacial cycle millennial scale variability; either through an amplitude modulation of the slow manifold based on obliquity paced variations as Roberts and Saha have done or the time dependant variation of the linear nullcline using CO2 as the authors have done here.

The legend for t0,t1,t2,t3 in Figure 8 looks incomplete. 

I like figure 8b , I would almost like to see the 4 curves illustrated separately as the red dominates. I’m not sure if there is an easy way to do this.

I like the section on the MPT , but the additional value seems to come from the incremental understanding achieved from relating it to more recent concepts from NDS and RDS. 

I don’t particularly think the title is completely appropriate , but I don’t have a good alternate suggestion. The authors  mention orbital insolation , but there are also internal mechanisms, plus a lot of discussion on NDS and RDS , but I’m not sure you can formulate this into an adequate short title.

To summarise, I think the authors have done an admirable job in bridging different timescales of Pleistocene climate variability using more recent mathematical concepts and adequately simple dynamical systems to illustrate their points.