I have produced 2 groups of time series data. Each group contains 100 time series, each of which is a solution to an ordinary differential equation where some parameters were allowed to vary normally and some were not (so mixed effects). So, the procedure of producing the data within each group went like this:

(1) Draw a certain number of parameters from their associated normal distribution with each parameter having its own associated mean and standard deviation (assume that these are not equal among parameters).

(2) Input these parameters together with the fixed parameters into a non-autonomous nonlinear ODE

(3) Solve ODE numerically, which produces a time series or a trajectory

(4) Repeat 100 times

Group 1 gives a scenario in which four parameters are allowed to vary normally each with their own mean equal to some fixed value.

Group 2 gives a scenario in which four parameters are allowed to vary normally each with their own mean equal to some fixed value, but the fixed mean for one of those parameters is different from the mean chosen for that parameter in group 1 (standard deviation is the same). The mean of the other three stochastic variables is the same as group 1, and all other parameters remain fixed.

I would like to know how to test if the set of time series produced by the group 1 is statistically different than the set of time series produced by the group 2.

I'm not sure how to go about performing this analysis and would appreciate any comments or suggestions on how to proceed.

(1) Draw a certain number of parameters from their associated normal distribution with each parameter having its own associated mean and standard deviation (assume that these are not equal among parameters).

(2) Input these parameters together with the fixed parameters into a non-autonomous nonlinear ODE

(3) Solve ODE numerically, which produces a time series or a trajectory

(4) Repeat 100 times

Group 1 gives a scenario in which four parameters are allowed to vary normally each with their own mean equal to some fixed value.

Group 2 gives a scenario in which four parameters are allowed to vary normally each with their own mean equal to some fixed value, but the fixed mean for one of those parameters is different from the mean chosen for that parameter in group 1 (standard deviation is the same). The mean of the other three stochastic variables is the same as group 1, and all other parameters remain fixed.

I would like to know how to test if the set of time series produced by the group 1 is statistically different than the set of time series produced by the group 2.

I'm not sure how to go about performing this analysis and would appreciate any comments or suggestions on how to proceed.

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