Example systems tracker

[kahaaga]

Systemssubmodule

This is a list of examples of dynamical systems with coupling between variables, either unidirectional or multidirectional, that can be studied in the framework of time series causality methods.

Contributing

Do you miss a system on the list? Open an issue for the wanted system and tag this tracker. Or, even better, implement the system yourself in theSystems submodule and do a pull request! You can use one of the existing example in the /systems/ subfolder as inspiration. Remember to add tests too!

Discrete maps

Unidirectional coupling

• [x] 2D logistic map. Unidirectional forcing from X to Y. [implemented in #6 ].
• [x] 3D logistic map. Three coupled systems with dynamical noise. From Runge, J. "Causal network reconstruction from time series: From theoretical assumptions to practical estimation." Chaos: An Interdisciplinary Journal of Nonlinear Science 28.7 (2018): 075310 [implemented in #5 ].
• [x] 2D Henon map. Unidirectional forcing from X to Y. [implemented in #8 ].
• [x] 4D Henon map. One 2D Henon subsystem unidirectionally driving another 2D Henon subsystem. From Krakovská, Anna, et al. "Comparison of six methods for the detection of causality in a bivariate time series." Physical Review E 97.4 (2018): 042207 [implemented in #15 ].
• [x] 3D vector autoregressive process. Unidirectional forcing X1 -> X2 - X3. From Papana, Angeliki, et al. "Simulation study of direct causality measures in multivariate time series." Entropy 15.7 (2013): 2635-2661..[implemented in #10 ].
• [ ] 2D unidirectionally coupled autogregressive processes of first order where one process contains a cosine. From Lungarella, Max, Alex Pitti, and Yasuo Kuniyoshi. "Information transfer at multiple scales." Physical Review E 76.5 (2007): 056117

  Strange, nonchaotic maps

• [x] 3D system where X is a highly nonlinear combination of Y and Z, which involves sine and cosine terms, respectively. From Verdes, P. F. "Assessing causality from multivariate time series." Physical Review E 72.2 (2005): 026222. [implemented in #32 ]
• [x] 2D map from equation 13 in Anishchenko, Vadim S., and Galina I. Strelkova. "Irregular attractors." Discrete dynamics in Nature and Society 2.1 (1998): 53-72.. [Implemented in #13]
• [x] 4D transitive causal chain of coupled logistic maps, X1 -> X2 -> X3 -> X4. Ye, Hao, et al. "Distinguishing time-delayed causal interactions using convergent cross mapping." Scientific reports 5 (2015): 14750 [implemented in #33]

Multidirectional

• [x] 2D bidirectionally coupled autoregressive processes of order 1. From Krakovská, Anna, et al. "Comparison of six methods for the detection of causality in a bivariate time series." Physical Review E 97.4 (2018): 042207. [implemented in #20]

Continuous systems

Unidirectional coupling

• [x] 6D Rössler-Rössler. One 3D Rössler system unidirectionally forcing another 3D Rössler subsystem. [implemented in #11 ]
• [x] 6D Rössler-Lorenz. One 3D Rössler system unidirectionally forcing a 3D Lorenz subsystem. From Krakovská, Anna, et al. "Comparison of six methods for the detection of causality in a bivariate time series." Physical Review E 97.4 (2018): 042207. [implemented in #14 ]
• [x] 3D Chua circuit system, w/ sine function nonlinearity. From [Tang, Wallace KS, et al. "Generation of n-scroll attractors via sine function." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48.11 (2001): 1369-1372](Tang, Wallace KS, et al. "Generation of n-scroll attractors via sine function." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48.11 (2001): 1369-1372.). [Implemented in #19 ]
• [x] 9D Lorenz system. Three coupled 3D Lorenz attractors with unidirectional forcing X1 -> X2 and X2 -> X3. [implemented in #22]

Multidirectional coupling

• [x] 6D Chua circuit system. One 3D Chua circuit forced by a sine function bidirectionally coupled to another 3D Chua circuit forced by a sine function. The subsystems are mutually coupled by a linear resistor. From Murali, K., and M. Lakshmanan. "Chaotic dynamics of the driven Chua's circuit." IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications 40.11 (1993): 836-840. [implemented in #18 ]

• [x] 9D Mediated link example. From Krakovská, Anna, et al. "Comparison of six methods for the detection of causality in a bivariate time series." Physical Review E 97.4 (2018): 042207. [implemented in #21]

• [x] Hindmarsh–Rose model of neuronal bursting. Hindmarsh, James L., and R. M. Rose. "A model of neuronal bursting using three coupled first order differential equations." Proc. R. Soc. Lond. B 221.1222 (1984): 87-102

[kahaaga]

The example systems will be reworked/reorganized. Some of the above systems may even be removed.