Validation of an Information Theoretic Measure of Locomotor Centralization Using Phase-Coupled Oscillator Models

Locomotor control differs in the degree of centralization: conceptually, the extent to which changes in local and global states are coupled. We recently developed a model-free mutual information-based centralization measure for animal and robotic systems. For this measure to be valid, it should reflect the centralization manifest in the network characteristics of phase-coupled oscillator models applied to locomotor data. We simulate and perturb a noisy six-oscillator system with preferred phase differences and network that produce the cockroach’s alternating tripod gait. We estimate the mutual information between perturbations and both single-oscillator and systemwide states (local and global responses). By varying the perturbations or networks we characterize the difference between local and global mutual information: our centralization measure. As network weighting increases, centralization increases irrespective of perturbation type. As network average clustering coefficient increases, centralization increases. This validation shows that our model-free measure predicts the behavior of a coupled oscillator model of cockroach locomotion, supporting general applicability of this centralization measure to living and engineered systems.