They are just rough sketches of 'aproaches' you could take to obtain the emulator. Both measure the current through the load by amplifying the the voltage across a shunt resistor, and use the obtained voltage to select what to connect to the output.
The first sketch depicts a mux (multiplexor) switching a different thevenin equivalent source to the load (Depending on the current, the voltage to the 2 comparators on the left will connect the mux input 0,1 or 3 to the mux output). To work out the correct thev. voltage and resistance, extend the lines on your transfer drawing until they intersect the y axis: this gives the thev. voltage; the thev. resistance for each region is given by the slope of the line within each region. There is 3 regions in your graph, hence 3 thevenin sources.
The second sketch uses a analogue to digital converter (ADC) to index a lookup table stored on an eprom to provide a programmed output voltage through a digital to analogue converter (DAC). The eprom may be programmed to give any weird transfer function you could think of.