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Chaotic oscillators are exciting sources for sound production due to their simplicity in implementation combined with their rich sonic output. However, the richness comes with difficulty of control, which is paramount to both their detailed understanding and in live musical performance. In this paper, we propose perceptually motivated parameter planes as a framework for studying the behavior of chaotic oscillators for musical use. Motivated by analysis via winding numbers, we extend traditional study of chaotic oscillators by using local features that are perceptually inspired. We illustrate the framework on the example of variations of the circle map. However, the framework is applicable for a wide range of sound synthesis algorithms with nontrivial parametric mappings.