Real-World Existence and Origins of the Spiral Organization of Shrimp-Shaped Domains

Abstract

In two-dimensional parameter spaces, nonlinear systems producing solutions of a fixed periodicity form islands of a characteristic shape, called "shrimp"-shaped domains (SSDs). In simulations of electronic circuits, SSDs of different periodicities were recently found to be connected along spirals. By means of a hardware realization of the simulations, we provide a first direct proof of the real-world existence of this phenomenon. An improved description establishes a close experiment-simulation correspondence, and a simplified circuit family demonstrates the homoclinic saddle-focus origin of the phenomenon.