CEoptim (version 1.3)

FitzHugh: Simulated data from FitzHugh-Nagumo differential equations

Description

The data correspond to the values V(t) of the FitzHugh-Nagumo differential equations

V'(t) = c*(V(t) - (V(t)^3)/3 + R(t))

R'(t) = -(1/c)*(V(t) - a + b*R(t))

at times 0, 0.05,..,20.0, with parameters a = 0.2, b = 0.2, c = 3 and initial conditions V(0) = -1, R(0)=1, and adding gaussian noise with standard deviation 0.5.

Usage

data(FitzHugh)

Format

A numeric vetor of length 401

References

Nagumo, J. and Arimoto, S. and Yoshizawa, S. (1962) An active pulse ransmission line simulating nerve axon, Proceedings of the IRE, 50 (10), 2061--2070.

Ramsay, J.O. and Hooker, G. and Campbell, D. and Cao J. (2007) Parameter estimation for differential equations: A generalized smoothing approach, Journal of the Royal Statistical Society, Series B 69 (5) 741--796.

Benham T., Duan Q., Kroese D.P., Liquet B. (2017) CEoptim: Cross-Entropy R package for optimization. Journal of Statistical Software, 76(8), 1-29.

Examples

## Plot the data
data(FitzHugh)
plot(FitzHugh,col="blue")