Here's one approach...

I1 is a current sink, pulling a variable current from 0 to 1A from the supply, through a sense resistor R1. U1/M1 act as a constant current source that aims to maintain the voltage across R1 at 10mV so the current it draws from V2 exactly mirrors the current drawn by I1,thus maintaining the load on V2 at 1A at all times..

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For those that want to argue I1 doesn't model the original question then here's a version that parametrically simulates a time-dependant resistor (R2) with the subcircuit I1+R3

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Can you include the files of this simulation?

 

Sure...