A wire catalyzing a simple oscillatory exothermic reaction and subject to control of the average temperature may undergo symmetry breaking and produce multipeak or even aperiodic behavior. Analytical and numerical derivation of the bifurcation diagram of a wire composed of N equal homogeneous (space-independent) sections produced few bands of periodic solutions separated by domains of aperiodic motions. A unique stable oscillatory solution was encountered at every set point. An actual uniform wire is expected to exhibit a similar structure. These results are compared with the structures observed during catalytic oxidation and electrochemical dissolution reactions using wires subject to constant average temperature or current, respectively.