Neuromodulation supports robust rhythmic pattern transitions in degenerate central pattern generators with fixed connectivity

Many essential biological functions, such as breathing and locomotion, rely on the coordination of robust and adaptable rhythmic patterns, governed by specific network architectures known as connectomes. Rhythmic adaptation is often linked to slow structural modifications of the connectome through synaptic plasticity, but such mechanisms are too slow to support rapid, localized rhythmic transitions. Here, we propose a neuromodulation-based control architecture for dynamically reconfiguring rhythmic activity in networks with fixed connectivity. The key control challenge is to achieve reliable rhythm switching despite neuronal degeneracy, a form of structured variability where widely different parameter combinations produce similar functional output. Using equivariant bifurcation theory, we derive necessary symmetry conditions on the neuromodulatory projection topology for the existence of target gaits. We then show that an adaptive neuromodulation controller, operating in a low-dimensional feedback gain space, robustly enforces gait transitions in conductance-based neuron models despite large parametric variability. The framework is validated in simulation on a quadrupedal gait control problem, demonstrating reliable gallop-to-trot transitions across 200 degenerate networks with up to fivefold conductance variability.