generate.panel.2order {doremi} | R Documentation |

`generate.panel.2order`

Generation of second order differential equation solutions for several individuals with intra-individual and inter-individual noise.
The function generates the equation coefficients following a normal distribution based on the parameter internoise and the coefficients provided as input.
It then calls the function `generate.2order`

to generate a solution of a second order differential equation with these parameters for the nind individuals.
Finally it adds measurement noise to each signal according to the value of the parameter intranoise.

```
generate.panel.2order(
time,
excitation = NULL,
y0 = 1,
v0 = 0,
t0 = NULL,
xi = 0.1,
period = 10,
k = 1,
yeq = 0,
nind = 1,
internoise = 0,
intranoise = 0
)
```

`time` |
is a vector containing the time values corresponding to the excitation signal. |

`excitation` |
Is a vector containing the values of the excitation signal. |

`y0` |
is the initial condition for the variable y(t=t0), (0, by default), it is a scalar. |

`v0` |
is the initial condition for the derivative dy(t=t0), (0, by default), it is a scalar. |

`t0` |
is the time corresponding to the initial condition y0 and v0. Default is the minimum value of the time vector. |

`xi` |
is the damping factor. A negative value will produce divergence from equilibrium. |

`period` |
is the period T of the oscillation, |

`k` |
Default is 1. It represents the proportionality between the stationary increase of signal and the excitation increase that caused it. Only relevant if the excitation is non null. |

`yeq` |
is the signal equilibrium value, i.e. the stationary value reached when the excitation term is 0. |

`nind` |
number of individuals. |

`internoise` |
Is the inter-individual noise added. The damping factor across individuals follows a normal distribution centered on the input parameter xi with a standard deviation of internoise*xi. The same applies to the other coefficients of the differential equation (T,k and yeq) and to the initial conditions (y0 and v0) |

`intranoise` |
Is the noise to signal ratio: dynamic noise added to each signal defined as the ratio between the variance of the noise and the variance of the signal |

Used for simulations in the context of the package.

Returns a data frame with signal and time values for the time and excitation vectors provided. It contains the following columns:

id - individual identifier (from 1 to nind).

excitation - excitation signal provided as input

time - time values provided as input

signalraw - signal with no noise (inter noise added for each individual)

signal - signal with intra noise added

`generate.2order`

for calculation of the numerical solution to the second order differential equation
and `generate.excitation`

for excitation signal generation

```
generate.panel.2order(time = generate.excitation(3, 6, 2, 1, 200, 2)$t,
excitation = generate.excitation(3, 6, 2, 1, 200, 2)$exc,
xi = 0.1,
period = 0.5,
k = 1,
nind = 5,
internoise = 0.2,
intranoise = 0.1)
```

[Package *doremi* version 1.0.0 Index]