Stable asymmetric states may be induced in catalytic wires controlled to attain a preset average temperature by changing the current fed into it. Complex multiplicity patterns are found there even at a fixed average temperature, A single-valued rate expression induces two bistability domains in a uniform wire. Cooling effects at the wire edge may eliminate one of these domains. Apparent isothermal tristability may be found with a multivalued rate curve but boundary effects destroy one of the solutions. Review of published multiplicity patterns observed with catalytic wires shows that isolated branches are due to the asymmetry. Analysis of more intricate kinetic models accounts for the bifurcation diagrams and maps observed during olefins oxidation on a Pt wire (part 2 of this work).