Explosive transitions in aging dynamics of coupled Hindmarsh-Rose neurons with distance-dependent interactions

Abstract

The abrupt onset of deterioration can have a profound impact on real-world situations, making it crucial to understand this process in order to prevent such events before they arise. In particular, understanding the dynamics of explosive transitions and aging behaviors in neural systems is essential for mitigating harmful illnesses. Importantly, we focus on such phenomena in coupled systems with distance-dependent interactions. Therefore, we primarily investigate the aging dynamics of globally coupled Hindmarsh-Rose (HR) neurons with distance-dependent interactions, concentrating on key factors such as coupling strength, inactive ratio, and decay rate that drive transitions between oscillatory and aging states. Through the use of the amplitude order parameter and bifurcation analysis, we identify the emergence of aging behaviors. Our findings show that increasing both the coupling strength and inactive ratio expands the aging region, while higher decay rates reverse aging dynamics by restoring rhythmic behavior. Importantly, we demonstrate bistability between aging (AG) and cluster oscillatory states (COS), exhibiting hysteresis characteristics. These results are validated through bifurcation and basin of attraction analysis, confirming the coexistence under varying initial conditions using a reduced model approach. Additionally, we explore the existence of explosive transitions and aging dynamics within complex network topologies, including small-world and random interactions. These findings significantly enhance our understanding of aging mechanisms in neural networks, with broader implications for brain aging, neuronal dysfunction, and other biological systems.