Energetic regulation of spiral waves by time delays and higher-order interactions

Spiral waves are recognized as crucial dynamical patterns in neural systems, whose aberrant activity is associated with neurological disorders such as epilepsy. Achieving energy-efficient control of spiral waves remains a significant challenge. In this study, the regulatory effects of time delays and higher-order interactions on the energy cost of spiral wave control are systematically investigated. Based on a Hindmarsh-Rose neuronal network with time delays, an energy function is introduced to quantify neuronal energy expenditure, and an energy efficiency index is defined. The results indicate that the spatiotemporal coherence of spiral waves is progressively disrupted by time delays, and structural collapse is induced once a critical delay threshold is exceeded. Higher-order interactions are shown to exhibit a biphasic regulatory effect. Moderate interaction strengths enhance spiral wave stability, whereas excessive strengths lead to dynamic instability. Energy analysis further reveals a transient metabolic compensation in the system prior to wave collapse. These findings uncover a coupling mechanism between spatiotemporal dynamics and energy metabolism in neural networks, providing novel insights into the relationship between brain activity patterns and energy constraints.