This work presents the first coherent two-dimensional diagram of complex dynamic behavior in a heterogeneous reacting system: the anodic dissolution of a nickel wire in sulfuric acid under galvanostatic conditions. Periodic, quasi-periodic, and chaotic states are identified, characterized, and mapped in the plane of current vs acid concentration. Most of the domain of complex behavior is composed of multipeak periodic solutions organized in bands differing in their winding number. The low-current transition to simple periodicity occurs through quasi-periodicity evident from the power spectrum and the angular return map. Two bands of chaotic solutions exist: one within the complex domain and another at its other boundary. Chaos is characterized by a high (>3) correlation dimension. The domain of simple periodicity is bounded by the Hopf and saddle-loop bifurcations. When the observed structure is compared with existing theories, it shows partial similarity with the structure of an oscillator subject to an external periodic force (the circle map). This similarity suggests possible mechanisms to account for the complex motion.