Aging transition in weighted homogeneous and heterogeneous networks

A network consisting of active and inactive dynamical units experiences aging transition as the number of inactive nodes in the network is increased gradually. In this work, we investigate aging transition by exploring the tenacity of network's global oscillation, implemented by considering a weighted network, while the weights are chosen randomly from a uniform distribution. We examine how the critical transition point from oscillatory to non-oscillatory dynamics changes as the width of the distribution is varied. Exact value of the parameter at which the transition occurs is derived analytically, and interestingly it is found to be dependent on the mean weight of the network. Moreover, we observe a correlation between the results for weighted and unweighted cases. The analysis is performed for both Stuart-Landau limit cycle oscillator network and chaotic Hindmarsh-Rose neuronal network organized in the framework of global (homogeneous) and scale-free (heterogeneous) architectures. Copyright (C) EPLA, 2020