Abstract: Rhythmic activity in neuronal networks underlies a wide range of repetitive behaviors essential for survival, including locomotion. While local circuits may generate oscillatory patterns, their functional impact often depends on interactions across neural populations and their response to feedback from the behaviors they control. Due to its experimental accessibility and diverse stepping patterns, stick insect locomotion provides a valuable model for studying rhythm generation and control. This work focuses on locomotion patterns generated by central pattern generators (CPGs) in the stick insect's middle leg. CPGs are neural networks connected by nonlinear chemical synapses that produce rhythmic patterns without input from sensory organs or higher control centers. Using an 18-dimensional system of coupled ODEs, we first identify the generation of specific stepping rhythms observed in stick insects. Then, we leverage fast-slow decomposition and analyze the dynamic mechanisms responsible for generating these rhythms. Finally, we relate these underlying dynamics to the degree of robustness and adaptability of these patterns in response to parameter changes. This study not only deepens our understanding of rhythm generation in locomotion but also offers insights that extend to other rhythm-generating neuronal systems.