Organized List of Questions
What is mulitfractal? (“the heart rate is nonchaotic, nonlinear, and multifractal.”, 18
Can you explain the difference between patchwork models and global models? (Freitas & Letellier)
What are the global models that Freitas and Letellier are using to test their ideas? The Rossler system? Is it purely theoretical or does it have a basis in some natural phenomena?
How is the maximum eddy turnover time different than the advection/diffusion timescale?
Can you clarify what types of nonlinear filtering are important in differentiating chaotic/stochastic systems?
Modeling and detecting chaos
Some of this week’s papers focus on chaos. Do you agree that deterministic chaos is widespread in nature? Even if not, how can considerations of noise help in complex systems research on cycles and steady states?
Freitas & Letellier (2009) say global modeling refers to getting a single model for reproducing chaotic dynamics. Is this for modeling one “module” of a complex system or should it apply on multiple scales?
“the noise titration test can give a positive indicator for chaos, even in systems in which there is not sensitive
dependence to initial conditions (Glass, 2009)”. Which is the difference between these concept of chaos (not sensitive to initial conditions) and stochastic concept?
Freitas & Letellier cite the following as the determining characteristics of chaos: sensitivity to initial conditions; boundedness; recurrence. Why are these the determining characteristics of chaos? Are there other characteristics that should be considered? What would Glass (or the authors he draws on) have to say about this?
Why is boundedness an easy assumption?
Chaotic behavior is always organized around periodic orbits? Recurrence corresponds to the bounds of a bifurcation diagram?
How is ‘linearized’ deterministic dynamics not evidence for determinism? This is not evidence for chaos, certainly, but isn’t this example by definition deterministic?
How is a limit cycle not regular? Why is folding an ingredient for producing chaos?
Freitas and Letellier say that we cannot distinguish chaotic behaviors from randomness using statistical analysis. Can we positively identify chaotic systems or do they even exist?
In Freitas and Letellier, how is a global model the ultimate test for determinism (because you can see if the model results and the experiment results exactly match, with no stochasticism at play)? They say “Getting periodic orbits from short time series necessarily requires the estimation of a global model which can then be integrated over a long time.” How does this discussion time scales relate to Jerolmack and Paola’s discussion of nonstationary regime (tTx)? If t>Tx, is the system deterministic?
Chaotic vs. non-chaotic systems
How can we conceptualize a non-chaotic, nonlinear, multifractal system? How does this relate/compare to other kinds of systems we have looked at the associated methods of analysis?
Exploring other aspects of a system besides whether or not it is chaotic may yield insights into system processes. (Why/not) is the question of whether or not a system is chaotic the right question?
Glass says that real systems are never fully deterministic, does that mean they are not fully chaotic? Can a system be semi-chaotic (i.e. displays chaotic dynamics)?
How does the differentiation between stochastic and chaotic systems affect systems management practices?
2) What can one do when a noise titration test gives a positive indicator for chaos to ensure it is describing truly chaotic dynamics?
Using a nonlinearity detection as a prior step for global modeling U. S. Freitas & C. Letellier
“Usually, low dimensional dynamics means that the behavior can be described in a phase space whose dimension is roughly less than ten.” Please explain the significance of this observation.
Will this procedure work for all types of chaotic time series? How do we know from this paper?
Noise/nature of noise
Which is an example of noise in an ecosystem and how can you measure the noise in one ecosystem?
Glass (2009) describes controversy over research finding signs of chaos in cardiac experiments, but not in realistic settings. 1) Do we face similar challenges when we do experiments to look for explanations of how systems really work?
Examining signal/noise in experimental conditions is one method for gaining insight into how to apply these methods to real systems. What are the potential pitfalls of the translation of experimental methods to real systems?
Glass states the “need for sharp predictions based on understanding fundamental mechanisms that are translated into clinically useful procedures” and raises a “promising direction that emerged from a non-linear dynamics perspective.” However, he notes that the application of this insight to clinically useful procedures is difficult. Does this challenge the usefulness of the approach?
We’ve talked a lot about being on the edge of chaos; how does our understanding of resonances aide in stability analysis?
Morphodynamic turbulence and system-clearing events
Jerolmack and Paola (2010):“it is unlikely that morphodynamic turbulence is a dissipative effect like the turbulent energy cascade of a fluid”, but are the “system‐clearing”events part of this dissipative effect or not?
How do ‘system clearing ‘ events described in J&P relate to chaos and self-organized complexity? It’s a threshold that overwhelms the autogenic dynamics and impacts the entire scale (spatial scale?) of the system, but is it a temporary disturbance (that is distinctly identifiable/measurable?), does it signal a phase change, a collapse?
Implications of Jerolmack and Paola
What are some of the implications for climate change research based on Jerolmack and Paola’s (2010) study on shredding of environmental signals by sediment transport?
What do J&P’s conclusions imply about our ability to detect geomorphic responses to climate change (i.e. will sediment transport rates change, by how much, with what impact….are these detectable/measurable)?
The paper has clear implications for interpreting th sedimentary record, but can “morphodynamic turbulence” also be used to predict the frequency of avulsions or landslides from time series, similar to the way that analysis of the heart rate could predict heart failure?
How does this shift in understanding of the signal persistence in sediment transport systems affect the scholarship to date? How does it impact the ability to examine the effects of rapid forcings? How does this apply to forcings that are constant over long timescales or pulse forcings with long fallouts (hydro-mining)?