There are two variants of this circuit. In the straightforward double potential well circuit, a summing amplifier adds the drive, the output of a comparator fed from the second of two integrators, and the outputs of each integrator in appropriate amounts; it delivers output to the first integrator and to an output of the system. The other output of the system is taken between the integrators; inverters are placed where necessary. Phase plane portraits are easily obtained by display of the two outputs as an x-y plot on an oscilloscope.
Figure 2 shows a block diagram of the doublewell system electronics, and the variant of the Extended Impact Oscillator whose maths are sketched in Figure 1. Figure 3 shows the modification required to synchronise two such systems, and also the circuit of the doublewell version.
Figure 2: Electronic implementations
Below is the synchronisation circuitry and the complete circuit diagram of the doublewell oscillator.
Figure 3: A synchronisation modification and the circuit diagram
In the extended impact oscillator, the output of the comparator is used additionally to invert the drive input when the displacement is in the RH plane. It is simple to see that the equations for an offset impact oscillator are isomorphic with this case; to derive the impact system phase plane portrait one rotates the double sided portrait around the origin by 180 degrees, superposes the original and the rotation, and ignores the motion x>0.
It is helpful to run the system quite slowly; the comparator takes time to switch. On an analogue oscilloscope a few tens of Hz are appropriate to make use of the persistence of vision. One can go slower if using a digitising storage instrument. Since large period solutions are easily obtained it also helps to have an indication of the state of the comparator; in our construction this drives a flashing LED.