I am aware of some examples of such cases but they are very rare. For example the attached figure shows period-doubling route to chaos based on the real data (for more details about this figure see [1, 2]).
Can you introduce me some references demonstrating “period-doubling route to chaos” in a REAL biological system? I especially appreciate if someone can help in obtaining proper dataset.
Thank you,
Sajad
[1] D.W. Crevier, M. Meister, Synchronous period-doubling in flicker vision of salamander and man, Journal of Neurophysiology, 79 (1998) 1869-1878.
[2] R. Falahian, M.M. Dastjerdi, M. Molaie, S. Jafari, S. Gharibzadeh, Artificial neural network-based modeling of brain response to flicker light, Nonlinear Dynamics, 81 (2015) 1951-1967.
Hi
Yes, Ca2+ realease in cardiac cells in certain conditions has this kind of behaviour.
In probably 1973, my former gymnasium teacher in biology showed me an article dealing with the development of the sheep population in New Zealand, where period doubling was evident. This reference would certainly be interesting for you. Sad to say that I have lost this reference.
So if anyone from the community is aware of, or can find, this article, please pass the reference on to me. I would very much appreciate !
Here you can see a paper that considers an application of the classical nonlinear-difference equation (with complex dynamics) on carcinogenesis:
http://www.sciencedirect.com/science/article/pii/S0165460801006653
There is eveidence of period doubling in infant respiration. Check the book "Dynamics of Biological Systems" by Michael Small.
The following may also be of interest. Frequency doubling in the temporal domain produces visible spatial periodicity at 2f when looking at sinusoidal grating patterns under some circumstances. The paper did not however discuss any transition to a chaotic domain of behaviour.
Parker, A., (1983). The effects of temporal modulation on the perceived spatial structure of sine-wave gratings. Perception, 12: 663-682.
A good example with some clear graphics is found here: Controlling Cardiac Chaos (Science 257, 1230 (1992))
I'm sorry for being slow to respond. I know an article about neurons.
"Biological Experimental Observations of an Unnoticed Chaos of Simulated by the Hindmarsh-Rose Model" - DOI: 10.1371 / journal.pone.0081759
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0081759
I hope this helps.
another,
Nonlinear Dynamics 78 (1), 391-407 (2014)
"Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models"
Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns. Cognitive Neurodynamics, 2012, 6(1): 89–106.
The only thing that comes to mind is this:
Costantino, R.F., Cushing, J.M., Dennis, B., Desharnais, R.A., Experimentally induced
transitions in the dynamic behavior of insect populations. Nature 375, 227–230 (1995).
Perhaps you could find others by searching for papers that cite this one.
This one is another good example of cardiac chaos with clear demonstrations of period-doubling cascades:
http://www.ncbi.nlm.nih.gov/pubmed/2304537
Alternate bearing of citrus is a typical example of nonlinear dynamics in agriculture. Based on the experimental data set, period-doubling route were demonstrated in the following articles.
Ye & Sakai, A new modified resource budget model for nonlinear dynamics in citrus production,Chaos ,Solitons and Fractals,87,51-60,2016
Ye & Sakai, Limited and time-delayed internal resource allocation generates oscillations and chaos in the dynamics of citrus crops,Chaos23,043124,2013
Prasad & Sakai,Understanding the Alternate Bearing Phenomenon: Resource Budget Model,Chaos25(12),123102,2015
http://www.sciencedirect.com/science/article/pii/S0960077916300959
Article Understanding the Alternate Bearing Phenomenon: Resource Budget Model
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