The aging transition, where oscillator networks collapse from global oscillation to quiescence due to an increasing fraction of inactive units, is fundamental for understanding functional degradation and system resilience. We investigate how pairwise and higher-order interactions synergistically modulate this transition in globally coupled FitzHugh-Nagumo neurons. Through numerical simulations employing forward and backward scans of the fraction of excitable neurons, mimicking damage accumulation and recovery, respectively, we systematically analyze transition types, hysteresis, and the resulting spatiotemporal patterns.
With only pairwise interactions, the system exhibits explosive transitions in both forward and backward scans, forming a pronounced hysteresis loop. The critical threshold depends strongly on coupling strength: stronger coupling shifts the transition to fewer inactive neurons, reducing robustness by facilitating the rapid propagation of local inactivation. At moderate coupling, the system jumps to a partially oscillatory state, whereas sufficiently high coupling causes direct and complete global collapse.
Higher-order interactions fundamentally alter this behavior. Acting alone, they yield a single explosive transition: the forward path remains discontinuous, but the backward path becomes continuous, thereby completely eliminating hysteresis. When coexisting with pairwise interactions, higher-order coupling effectively suppresses hysteresis; increasing its strength progressively shrinks the hysteretic loop until it vanishes entirely, even amidst strong pairwise coupling.
Mapping the parameter space reveals that higher-order interactions not only reduce the hysteresis area but also progressively weaken the system's dependence on pairwise coupling strength, shifting the transition threshold to be primarily determined by the fraction of inactive neurons. Furthermore, they induce stable mixed states near the critical point, characterized by the robust coexistence of oscillatory and quiescent neurons. These intermediate states act as key dynamical buffers, preventing abrupt collapse and enabling continuous modulation from synchronization to quiescence.
This study demonstrates that higher-order interactions play a qualitatively distinct and indispensable role in regulating aging transitions: they enhance reversibility, suppress path dependence, enrich dynamical repertoires, and strengthen network resilience. Our findings provide new mechanistic insights into neural adaptation under aging or injury and highlight the critical importance of incorporating higher-order interactions in modeling complex biological systems.