Create random time series with shifts predetermined

I'm trying to create some random time series with shifts (or gap) along the series. Some with normal distribution and the others with non-normal distribution (Log normal for example). For both I have to decide:

• the numbers of the shifts
• the positions of each shifts
• the magnitudes of each shifts
• the lenght between a shift and another one

The data is 130 years length (monthly) with all positive numbers (because I want to simulate natural abundance time series). I hope with a picture you can understand better.

This is an example to understand what I want to create

I red in other questions some methods for example I tried with arima.sim() but I think that I can't put my shifts.

Please help me.

Thank you