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Networks of excitable elements are widely used to model real-world biological and social systems. The dynamic range of an excitable network quantifies the range of stimulus intensities that can be robustly distinguished by the network response, and is maximized at the critical state. In this study, we examine the impacts of backtracking activation on system criticality in excitable networks consisting of both excitatory and inhibitory units. We find that, for dynamics with refractory states that prohibit backtracking activation, the critical state occurs when the largest eigenvalue of the weighted non-backtracking (WNB) matrix for excitatory units, $lambda^E_{NB}$, is close to one, regardless of the strength of inhibition. In contrast, for dynamics without refractory state in which backtracking activation is allowed, the strength of inhibition affects the critical condition through suppression of backtracking activation. As inhibitory strength increases, backtracking activation is gradually suppressed. Accordingly, the system shifts continuously along a continuum between two extreme regimes -- from one where the criticality is determined by the largest eigenvalue of the weighted adjacency matrix for excitatory units, $lambda^E_W$, to the other where the critical state is reached when $lambda_{NB}^E$ is close to one. For systems in between, we find that $lambda^E_{NB}<1$ and $lambda^E_W>1$ at the critical state. These findings, confirmed by numerical simulations using both random and synthetic neural networks, indicate that backtracking activation impacts the criticality of excitable networks.
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at
Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here collective excitability and self-sustained bursting oscillations are shown t
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing driving external fields $h rightarrow 0$. Considering that this is rarely the case for natural systems, such a restriction
Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks.
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network topology b