Fast–slow dynamics and spike organization in the electromechanical gyrostat system: Unveiling the intricacies of shrimp structures

This paper investigates the nonlinear dynamics of an electromechanical gyrostat system, focusing on the timescale characteristics of the system's fast variables. Through three kinds of complementary stability diagrams, the complex dynamical structures, particularly the formation and organization of the well-known "shrimp" structures, are unfolded in the parameter space. The research identifies significant differences in the rates of the system's fast variables, which directly affect the distribution of spikes and explain the diversity in the internal spike distribution of shrimps. These findings provide new insights and a theoretical foundation for understanding and controlling complex behaviors in nonlinear dynamical systems. This work is also developed further on the foundation of the pioneering work by Professor Jason A. C. Gallas, as a tribute to his outstanding contributions to the field of nonlinear dynamics.