Many real world applications are of time-varying nature and an online learning algorithm is preferred in tracking the realtime changes of the time-varying system. Online sequential extreme learning machine (OSELM) is an excellent online learning algorithm, and some improved OSELM algorithms incorporating forgetting mechanism have been developed to model and predict the time-varying system. But the existing algorithms suffer from a potential risk of instability due to the intrinsic ill-posed problem; besides, the adaptive tracking ability of these algorithms for complex time-varying system is still very weak. In order to overcome the above two problems, this paper proposes a novel OSELM algorithm with generalized regularization and adaptive forgetting factor (AFGR-OSELM). In the AFGR-OSELM, a new generalized regularization approach is employed to replace the traditional exponential forgetting regularization to make the algorithm have a constant regularization effect; consequently the potential illposed problem of the algorithm can be completely avoided and a persistent stability can be guaranteed. Moreover, the AFGR-OSELM adopts an adaptive scheme to adjust the forgetting factor dynamically and automatically in the online learning process so as to better track the dynamic changes of the time-varying system and reduce the adverse effects of the outdated data in time; thus it tends to provide desirable prediction results in time-varying environment. Detailed performance comparisons of AFGR-OSELM with other representative algorithms are carried out using artificial and real world data sets. The experimental results show that the proposed AFGR-OSELM has higher prediction accuracy with better stability than its counterparts for predicting time-varying system.

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To investigate the effect of electromagnetic induction on the electrical activity of neuron, the variable for magnetic flow is used to improve Hindmarsh–Rose neuron model. Simultaneously, due to the existence of time-delay when signals are propagated between neurons or even in one neuron, it is important to study the role of time-delay in regulating the electrical activity of the neuron. For this end, a four-variable neuron model is proposed to investigate the effects of electromagnetic induction and time-delay. Simulation results suggest that the proposed neuron model can show multiple modes of electrical activity, which is dependent on the time-delay and external forcing current. It means that suitable discharge mode can be obtained by selecting the time-delay or external forcing current, which could be helpful for further investigation of electromagnetic radiation on biological neuronal system.