A decrease in alpha band power is defined as a hallmark of electroencephalogram (EEG) in Alzheimer's disease (AD). This study devotes to understanding the neuronal correlates of alpha rhythm slowing associated with AD from the view of neurocomputation. Firstly, a modified computational model of thalamo-cortico-thalamic (TCT) circuitry is constructed by incorporating two important biologically plausible ingredients. One is the disinhibition property between different inhibitory interneurons in the cortical module. The other is the full relay function of thalamic relay nucleus (TCR) to the cortical module. Then, by decreasing synaptic connectivity parameters to mimic the neuropathological condition of synapse loss in AD, the correlation between neuronal synaptic behavior and abnormal alpha rhythm is simulated by means of power spectral analysis. The results indicate that these decreases of synaptic activity, i.e., not only the excitatory synaptic connections from TCR to fast inhibitory interneurons C fte and from excitatory interneurons to pyramidal neurons C pxe but also the inhibitory synaptic connections from fast inhibitory interneurons to slow inhibitory interneurons C lfi and from inhibitory interneurons to TCR C tii , can significantly diminish the peak power density over the alpha band of the thalamic output, which implies that there is a slowing of alpha band. Furthermore, the underlying mechanism behind the alpha rhythmic changes is analyzed using nonlinear dynamical technique. The results reveal that decreases of C fte , C pxe , C lfi and C tii can make the thalamic module transfer from a limit cycle mode to a point attractor mode, which may lead to the alpha rhythm slowing in the modified TCT model. We expect this work can be helpful in identifying early biomarkers of AD's EEG and understanding potential pathogenesis of AD.

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Explosive death phenomenon has been gradually gaining attention of researchers due to the research boom of explosive synchronization, and it has been observed recently for the identical or nonidentical coupled systems in all-to-all network. In this work, we investigate the emergence of explosive death in networked Van der Pol (VdP) oscillators with conjugate variables coupling. It is demonstrated that the network structures play a crucial role in identifying the types of explosive death behaviors. We also observe that the damping coefficient of the VdP system not only can determine whether the explosive death state is generated but also can adjust the forward transition point. We further show that the backward transition point is independent of the network topologies and the damping coefficient, which is well confirmed by theoretical analysis. Our results reveal the generality of explosive death phenomenon in different network topologies and are propitious to promote a better comprehension for the oscillation quenching behaviors.

We study the effect of noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonic PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR.

In this paper, the effects of random errors on the oscillating behaviors have been studied theoretically and numerically in a prototypical coupled nonlinear oscillator. Two kinds of noises have been employed respectively to represent the measurement errors accompanied with the parameter specifying the distance from a Hopf bifurcation in the Stuart-Landau model. It has been demonstrated that when the random errors are uniform random noise, the change of the noise intensity can effectively increase the robustness of the system. While the random errors are normal random noise, the increasing of variance can also enhance the robustness of the system under certain conditions that the probability of aging transition occurs reaches a certain threshold. The opposite conclusion is obtained when the probability is less than the threshold. These findings provide an alternative candidate to control the critical value of aging transition in coupled oscillator system, which is composed of the active oscillators and inactive oscillators in practice.