Numerous vital biological functions, including breathing, digestion, and walking, rely on the orchestration of robust and adaptable rhythmic patterns. Bursting inhibitory neural circuits have traditionally been acknowledged as the cornerstone responsible for initiating and regulating these patterns. Various rhythmic patterns have been associated with distinct network architectures, known as connectomes. However, these networks often suffer from vulnerability to disruption, limited flexibility, and difficulties in external manipulation due to their static nature. These limitations become particularly evident when living organisms require rapid and localized transitions in rhythmic patterns, which cannot solely rely on synaptic connectivity changes through plasticity. In our study, we propose a novel approach to address this challenge: integrating neuromodulation to enable the dynamic pattern reconfiguration of fixed connectome networks of conductance-based models. By introducing a neuromodulatory network beside a rhythmic network, which encodes various patterns in its connectome, we can facilitate seamless transitions from one pattern to another. This transition occurs through the modulation of specific neuromodulatory neurons, switching them from bursting to tonic firing and vice versa. Notably, despite the variation in neuronal parameters, the pattern shift remains robust. One noteworthy application of our research concerns locomotion regulation. We demonstrate the practical implications of our approach within the context of quadruped gait control, specifically in the trot-to-gallop transition. This innovative approach allows us to dissect the trot and gallop rhythms hardwired by the connectome, while enabling external modulation through neuromodulatory mechanisms. The implications of this work aim at generality, with various applications in computational neuroscience.