Dynamical Models of Electric Arcs and Memristors: The Common Properties

We discuss the memristive properties (or fingerprints) of the hybrid Cassie-Mayr model of electric arcs. In particular, we prove that: 1) the voltage-current characteristic of the model has the pinched hysteresis nature; 2) the voltage and current zero crossings occur at the same instants; and 3) when the frequency f of the power supply increases, the voltage-current pinched hysteresis characteristic tends closer to a single-valued one, meaning that the voltage-current graph becomes that of a resistor (with an increased linearity for f -> infinity). The conductance g of the Cassie-Mayr model decreases when the frequency increases. The hybrid Cassie-Mayr model describes, therefore, an interesting case of a memristive phenomenon.