Datasets (reservoirpy.datasets)

Chaotic timeseries on continuous time

Timeseries expressing a chaotic behaviour and defined on a continuous time axis, generated at will.

All timeseries defined by differential equations on a continuous space are by default approximated using 4-5th order Runge-Kuta method [1], either homemade (for Mackey-Glass timeseries) or from Scipy scipy.integrate.solve_ivp() tool.

mackey_glass(n_timesteps[, tau, a, b, n, ...])	Mackey-Glass timeseries [8] [9], computed from the Mackey-Glass delayed differential equation.
lorenz(n_timesteps[, rho, sigma, beta, x0, h])	Lorenz attractor timeseries as defined by Lorenz in 1963 [6] [7].
multiscroll(n_timesteps[, a, b, c, x0, h])	Double scroll attractor timeseries [10] [11], a particular case of multiscroll attractor timeseries.
doublescroll(n_timesteps[, r1, r2, r4, ir, ...])	Double scroll attractor timeseries [10] [11], a particular case of multiscroll attractor timeseries.
rabinovich_fabrikant(n_timesteps[, alpha, ...])	Rabinovitch-Fabrikant system [12] [13] timeseries.
lorenz96(n_timesteps[, warmup, N, F, dF, h, x0])	Lorenz96 attractor timeseries as defined by Lorenz in 1996 [17].
rossler(n_timesteps[, a, b, c, x0, h])	Rössler attractor timeseries [18].
kuramoto_sivashinsky(n_timesteps[, warmup, ...])	Kuramoto-Sivashinsky oscillators [19] [20] [21].

Chaotic timeseries on discrete time

Timeseries expressing a chaotic behaviour and defined on a discrete time axis, generated at will.

Discrete timeseries are defined using recurrent time-delay relations.

logistic_map(n_timesteps[, r, x0])	Logistic map discrete timeseries [4] [5].
henon_map(n_timesteps[, a, b, x0])	Hénon map discrete timeseries [2] [3].
narma(n_timesteps[, order, a1, a2, b, c, ...])	Non-linear Autoregressive Moving Average (NARMA) timeseries, as first defined in [14], and as used in [15].

Classification/pattern recognition tasks

Classified datasets of timeseries.

japanese_vowels([one_hot_encode, ...])

Load the Japanese vowels [16] dataset.

Miscellaneous

to_forecasting(timeseries[, forecast, axis, ...])	Split a timeseries for forecasting tasks.
set_seed(s)	Change the default random seed value used for dataset generation.
get_seed()	Return the current random state seed used for dataset generation.

References

[1]

Runge–Kutta methods on Wikipedia.

[2]

M. Hénon, ‘A two-dimensional mapping with a strange attractor’, Comm. Math. Phys., vol. 50, no. 1, pp. 69–77, 1976.

[3]

Hénon map on Wikipedia

[4]

R. M. May, ‘Simple mathematical models with very complicated dynamics’, Nature, vol. 261, no. 5560, Art. no. 5560, Jun. 1976, doi: 10.1038/261459a0.

[5]

Logistic map on Wikipedia

[6]

E. N. Lorenz, ‘Deterministic Nonperiodic Flow’, Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, Mar. 1963, doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;

[7]

Lorenz system on Wikipedia.

[8]

M. C. Mackey and L. Glass, ‘Oscillation and chaos in physiological control systems’, Science, vol. 197, no. 4300, pp. 287–289, Jul. 1977, doi: 10.1126/science.267326.

[9]

Mackey-Glass equations on Wikipedia.

[10] (1,2)

G. Chen and T. Ueta, ‘Yet another chaotic attractor’, Int. J. Bifurcation Chaos, vol. 09, no. 07, pp. 1465–1466, Jul. 1999, doi: 10.1142/S0218127499001024.

[11] (1,2)

Chen double scroll attractor on Wikipedia.

[12]

M. I. Rabinovich and A. L. Fabrikant, ‘Stochastic self-modulation of waves in nonequilibrium media’, p. 8, 1979.

[13]

Rabinovich-Fabrikant equations on Wikipedia.

[14]

A. F. Atiya and A. G. Parlos, ‘New results on recurrent network training: unifying the algorithms and accelerating convergence,‘ in IEEE Transactions on Neural Networks, vol. 11, no. 3, pp. 697-709, May 2000, doi: 10.1109/72.846741.

[15]

B.Schrauwen, M. Wardermann, D. Verstraeten, J. Steil, D. Stroobandt, ‘Improving reservoirs using intrinsic plasticity‘, Neurocomputing, 71. 1159-1171, 2008, doi: 10.1016/j.neucom.2007.12.020.

[16]

M. Kudo, J. Toyama and M. Shimbo. (1999). “Multidimensional Curve Classification Using Passing-Through Regions”. Pattern Recognition Letters, Vol. 20, No. 11–13, pages 1103–1111.

[17]

Lorenz, E. N. (1996, September). Predictability: A problem partly solved. In Proc. Seminar on predictability (Vol. 1, No. 1).

[18]

O.E. Rössler, “An equation for continuous chaos”, Physics Letters A, vol 57, Issue 5, Pages 397-398, ISSN 0375-9601, 1976, https://doi.org/10.1016/0375-9601(76)90101-8.

[19]

Kuramoto, Y. (1978). Diffusion-Induced Chaos in Reaction Systems. Progress of Theoretical Physics Supplement, 64, 346–367. https://doi.org/10.1143/PTPS.64.346

[20]

Sivashinsky, G. I. (1977). Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations. Acta Astronautica, 4(11), 1177–1206. https://doi.org/10.1016/0094-5765(77)90096-0

[21]

Sivashinsky, G. I. (1980). On Flame Propagation Under Conditions of Stoichiometry. SIAM Journal on Applied Mathematics, 39(1), 67–82. https://doi.org/10.1137/0139007