Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks.

Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis that are able to unveil many features that are hidden to more traditional analysis methods. In this work, we focus on one particular approach: the application of ordinal pattern transition networks for characterizing time series data. More specifically, we generalize a traditional statistical complexity measure (SCM) based on permutation entropy by explicitly disclosing heterogeneous frequencies of ordinal pattern transitions. To demonstrate the usefulness of these generalized SCMs, we employ them to characterize different dynamical transitions in the logistic map as a paradigmatic model system, as well as real-world time series of fluid experiments and electrocardiogram recordings. The obtained results for both artificial and experimental data demonstrate that the consideration of transition frequencies between different ordinal patterns leads to dynamically meaningful estimates of SCMs, which provide prospective tools for the analysis of observational time series.

Control analysis of electrical stimulation for epilepsy waveforms in a thalamocortical network.

Physiological experiments and computational models both show that the thalamic reticular nucleus (RE) participates in inducing various firing patterns of cortex. Absence seizure, featured by 2-4 Hz spike-wave discharges (SWD) oscillation, is a high incidence of disease in children. Lots of electrophysiological experiments have verified the correlation between absence seizures and RE, however, the dynamical mechanisms are not well understood. Based on previous Taylor model, we firstly study the effects of external input and self-inhibition of RE on epilepsy transition. We show that increasing external input and self-inhibition of RE can lead the system from epileptic state to normal state, and vice versa. Next, we explore two stimulus strategies added in RE and various transition behaviors can be induced, such as high saturated state to clonic. Meanwhile, as the intensity of stimulation increasing, they can not only suppress the SWD, but also produce tonic-clonic oscillation. Finally, the control of DBS on single neuron cluster and two neuron clusters are compared and we find stimulating RE and TC simultaneously is a superior mode to stimulate anyone of RE or TC. It is hoped that the results we obtained will have an enlightenment on clinical treatment.

Tuning coupling rate to control oscillation quenching in fractional-order coupled oscillators.

Introducing the fractional-order derivative into the coupled dynamical systems intrigues gradually the researchers from diverse fields. In this work, taking Stuart-Landau and Van der Pol oscillators as examples, we compare the difference between fractional-order and integer-order derivatives and further analyze their influences on oscillation quenching behaviors. Through tuning the coupling rate, as an asymmetric parameter to achieve the change from scalar coupling to non-scalar coupling, we observe that the onset of fractional-order not only enlarges the range of oscillation death, but attributes to the transition from fake amplitude death to oscillation death for coupled Stuart-Landau oscillators. We go on to show that for a coupled Van der Pol system only in the presence of a fractional-order derivative, oscillation quenching behaviors will occur. The results pave a way for revealing the control mechanism of oscillation quenching, which is critical for further understanding the function of fractional-order in a coupled nonlinear model.

Aging transition in mixed active and inactive fractional-order oscillators.

Recently, a large number of studies have concentrated on aging transition, but they have so far been restricted to coupled integer-order oscillators. Here, we report the first study of aging transition in mixed active and inactive fractional-order oscillators. It has been demonstrated that while the heterogeneity is caused by the distance parameter, both the coupling strength and the fractional-order derivative can modulate the critical ratio at which aging transition occurs. In addition, a small fractional-order derivative may ruin the ability of oscillation and, thus, reduce the critical ratio in globally coupled fractional-order Stuart-Landau oscillators. Remarkably, the larger the natural frequency is the more easily the aging transition occurs in coupled fractional-order oscillators. Further studies have shown that, being diverse from an integer-order Stuart-Landau oscillator, the natural frequency may induce a Hopf bifurcation in a fractional-order Stuart-Landau oscillator, accordingly, introducing a new heterogeneity in the coupled fractional-order Stuart-Landau oscillators. Therein, a counterintuitive phenomenon has been found that the critical ratio depends unmonotonously on the coupling strength, which implies that the coupled fractional-order Stuart-Landau oscillators possess the weakest robustness of oscillation at a certain level of coupling strength.

How synaptic plasticity influences spike synchronization and its transitions in complex neuronal network.

There is evidence that synaptic plasticity is a vital feature of realistic neuronal systems. This study, describing synaptic plasticity by a modified Oja learning rule, focuses on the effect of synapse learning rate on spike synchronization and its relative transitions in a Newman-Watts small-world neuronal network. The individual dynamics of each neuron is modeled by a simple Rulkov map that produces spiking behavior. Numerical results have indicated that large coupling can lead to a spatiotemporally synchronous pattern of spiking neurons; in addition, this kind of spike synchronization can emerge intermittently by turning information transmission delay between coupled neurons. Interestingly, with the advent of synaptic plasticity, spike synchronization is gradually destroyed by increasing synapse learning rate; moreover, the phenomenon of intermittent synchronization transitions becomes less and less obvious and it even disappears for relative larger learning rate. Further simulations confirm that spike synchronization as well as synchronization transitions is largely independent of network size. Meanwhile, we detect that large shortcuts probability can facilitate spike synchronization, but it is disadvantageous for delay-induced synchronization transitions.

Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators.

Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.

Autapse-induced multiple stochastic resonances in a modular neuronal network.

This study investigates the nontrivial effects of autapse on stochastic resonance in a modular neuronal network subjected to bounded noise. The resonance effect of autapse is detected by imposing a self-feedback loop with autaptic strength and autaptic time delay to each constituent neuron. Numerical simulations have demonstrated that bounded noise with the proper level of amplitude can induce stochastic resonance; moreover, the noise induced resonance dynamics can be significantly shaped by the autapse. In detail, for a specific range of autaptic strength, multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted. These appropriately adjusted delays are detected to nearly approach integer multiples of the period of the external weak signal when the autaptic strength is very near zero; otherwise, they do not match the period of the external weak signal when the autaptic strength is slightly greater than zero. Surprisingly, in both cases, the differences between arbitrary two adjacent adjusted autaptic delays are always approximately equal to the period of the weak signal. The phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of the external weak signal and the intramodule probability of subnetwork. These findings could have important implications for weak signal detection and information propagation in realistic neural systems.

Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback.

The dynamics in fractional-order systems have been widely studied during the past decade due to the potential applications in new materials and anomalous diffusions, but the investigations have been so far restricted to a fractional-order system without time delay(s). In this paper, we report the first study of random responses of fractional-order system coupled with noise and delayed feedback. Stochastic averaging method has been utilized to determine the stationary probability density functions (PDFs) by means of the principle of minimum mean-square error, based on which stochastic bifurcations could be identified through recognizing the shape of the PDFs. It has been found that by changing the fractional order the shape of the PDFs can switch from unimodal distribution to bimodal one, or from bimodal distribution to unimodal one, thus announcing the onset of stochastic bifurcation. Further, we have demonstrated that by merely modulating the time delay, the feedback strengths, or the noise intensity, the shapes of PDFs can transit between a single peak and a double peak. Therefore, it provides an efficient candidate to control, say, induce or suppress, the stochastic bifurcations in fractional-order systems.

Delay-induced stochastic bifurcations in a bistable system under white noise.

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.

Modulating resonance behaviors by noise recycling in bistable systems with time delay.

In this paper, the impact of noise recycling on resonance behaviors is studied theoretically and numerically in a prototypical bistable system with delayed feedback. According to the interior cooperating and interacting activity of noise recycling, a theory has been proposed by reducing the non-Markovian problem into a two-state model, wherein both the master equation and the transition rates depend on not only the current state but also the earlier two states due to the recycling lag and the feedback delay. By virtue of this theory, the formulae of the power spectrum density and the linear response function have been found analytically. And the theoretical results are well verified by numerical simulations. It has been demonstrated that both the recycling lag and the feedback delay play a crucial role in the resonance behaviors. In addition, the results also suggest an alternative scheme to modulate or control the coherence or stochastic resonance in bistable systems with time delay.

Detecting stochastic multiresonance in neural networks via statistical complexity measure.

This paper employs statistical complexity measure (SCM) to investigate the occurrence of stochastic multiresonance (SMR) induced by noise and time delay in small-world neural networks coupled with FitzHugh-Nagumo (FHN) neurons. Our findings reveal that SCM exhibits four local maxima at four optimal noise levels, providing evidence for the occurrence of quadruple stochastic resonances. When time delay τ is taken into account in the information transmission, under moderate noise levels, SCM shows several local maxima when τ = n T e with n being a positive integer and T e being the period of subthreshold signal. This indicates the appearance of delay-induced SMR at the multiples of the period of subthreshold signal. Intriguingly, at low noise levels, a strong coherence between time delay and neuronal firing dynamics emerges at τ = n T e - 2 , as confirmed by a series of SCM maxima at these time delays. Furthermore, the study demonstrates that by adjusting the degrees and sizes of small-world networks, as well as the coupling strength, it is possible to optimize the strength of delay-induced SMR, thus maximizing the detection capability of subthreshold signal. The research results may provide us with an effective approach for understanding the role of time delay in signal detection and information transmission.

Complexity decline of hippocampal CA1 circuit model due to cholinergic deficiency associated with Alzheimer's disease.

A hallmark of Alzheimer's disease (AD) is cholinergic system dysfunction, directly affecting the hippocampal neurons. Previous experiments have demonstrated that reduced complexity is one significant effect of AD on electroencephalography (EEG). Motivated by these, this study explores reduced EEG complexity of cholinergic deficiency in AD by neurocomputation. We first construct a new hippocampal CA1 circuit model with cholinergic action. M-current IM and calcium-activated potassium current IAHP are newly introduced in the model to describe cholinergic input from the medial septum. Then, by enhancing IM and IAHP to mimic cholinergic deficiency, how cholinergic deficiency influences the model complexity is investigated by sample entropy (SampEn) and approximate entropy (ApEn). Numerical results show a more severe cholinergic deficit with lower model complexity. Furthermore, we conclude that the decline of SampEn and ApEn is due to the greatly diminished excitability of model neurons. These suggest that decreased neuronal excitability due to cholinergic impairment may contribute to reduced EEG complexity in AD. Subsequently, statistical analysis between simulated AD patients and normal control (NC) groups demonstrates that SampEn and auto-mutual-information (AMI) decrease rates significantly differ. Compared to NC, AD patients have a lower SampEn and a less negative AMI decline rate. These imply a low rate of new-generation information in AD brains with cholinergic deficits. Interestingly, the statistical correlation between SampEn and AMI is analyzed, and they have a large negative Pearson correlation coefficient. Thus, AMI reduction rates may be a complementary tool for complex analysis. Our modeling and complex analysis are expected to provide a deeper understanding of the reduced EEG complexity resulting from cholinergic deficiency.

Decreased coherence in the model of the dorsal visual pathway associated with Alzheimer's disease.

Decreased coherence in electroencephalogram (EEG) has been reported in Alzheimer's disease (AD) experimentally, which could be considered as a typical electrophysiological characteristic in AD. This work aimed to investigate the effect of AD on coherence in the dorsal visual pathway by the technique of neurocomputation. Firstly, according to the hierarchical organization of the cerebral cortex and the information flows of the dorsal visual pathway, a more physiologically plausible neural mass model including cortical areas v1, v2, and v5 was established in the dorsal visual pathway. The three interconnected cortical areas were connected by ascending and descending projections. Next, the pathological condition of loss of long synaptic projections in AD was simulated by reducing the parameters of long synaptic projections in the model. Then, the loss of long synaptic projections on coherence among different visual cortex areas was explored by means of power spectral analysis and coherence function. The results demonstrate that the coherence between these interconnected cortical areas showed an obvious decline with the gradual decrease of long synaptic projections, i.e. decrease in descending projections from area v2 to v1 and v5 to v2 and ascending projection from area v2 to v5. Hopefully, the results of this study could provide theoretical guidance for understanding the dynamical mechanism of AD.

Control of epileptic activities in a cortex network of multiple coupled neural populations under electromagnetic induction.

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.

Classification of Alzheimer's disease progression based on sMRI using gray matter volume and lateralization index.

Note that identifying Mild Cognitive Impairment (MCI) is crucial to early detection and diagnosis of Alzheimer's disease (AD). This work explores how classification features and experimental algorithms influence classification performances on the ADNI database. Based on structural Magnetic Resonance Images (sMRI), two features including gray matter (GM) volume and lateralization index (LI) are firstly extracted through hypothesis testing. Afterward, several classifier algorithms including Random Forest (RF), Decision Tree (DT), K-Nearest Neighbor(KNN) and Support Vector Machine (SVM) with RBF kernel, Linear kernel or Polynomial kernel are established to realize binary classification among Normal Control (NC), Early Mild Cognitive Impairment (EMCI), Late Mild Cognitive Impairment (LMCI) and AD groups. The main experimental results are as follows. (1) The classification performance in the feature of LI is poor compared with those in the feature of GM volume or the combined feature of LI and GM volume, i.e., the classification accuracies in the feature of LI are relatively low and unstable for most classifier models and subject groups. (2) Comparing with the classification performances in the feature of GM volume and the combined feature of LI and GM volume, the classification accuracy of NC group versus AD group is relatively stable for different classifier models, moreover, the accuracy of AD group versus NC group is almost the highest, with the most classification accuracy of 98.0909%. (3) For different subject groups, the SVM classifier algorithm with Polynomial kernel and the KNN classifier algorithm show relatively stable and high classification accuracy, while DT classifier algorithm shows relatively unstable and lower classification accuracy. (4) Except the groups of EMCI versus LMCI and NC versus EMCI, the classification accuracies are significantly enhanced by emerging the LI into the original feature of GM volume, with the maximum accuracy increase of 5.6364%. These results indicate that various factors of subject data, feature types and experimental algorithms influence classification performances remarkably, especially the newly introduced feature of LI into the feature of GM volume is helpful to improve classification results in some certain extent.

Effect of acetylcholine deficiency on neural oscillation in a brainstem-thalamus-cortex neurocomputational model related with Alzheimer's disease.

Previous works imply that involving brainstem in neuropathological studies of Alzheimer's disease (AD) is of clinically significant. This work constructs a comprehensive neural mass model for cholinergic neuropathogenesis that involves brainstem, thalamus and cortex, wherein how acetylcholine deficiency in AD affects neural oscillation of the model output is systematically explored from the perspective of neurocomputation. By decreasing synapse connectivity parameters in direct cholinergic pathway from brainstem to thalamus or in indirect glutamatergic synapse pathway from cortex to brainstem to mimic the pathological condition of reduced acetylcholine release in patients with AD, the property of neural oscillation in this model is numerically investigated by means of power spectrum in frequency domain and amplitude distribution in time domain. Simulated results demonstrate that decreasing synapse connectivity whether in the direct cholinergic pathway or in the indirect glutamatergic synapse pathway can alter the neural oscillation significantly in three aspects: it induces an obvious decrease of dominant frequency; it leads to a degraded rhythmic activity in the alpha frequency band as well as an enhanced rhythmic activity in the theta frequency band; it results in reduced oscillation amplitude of the model output. These results are agreement with the characteristic of electrophysiological EEG measurement recorded in AD, especially support the hypothesis that cholinergic deficiency is a promising pathophysiological origin of EEG slowing in AD. Our analysis indicates that targeting the cholinergic system may have potential prospects in early diagnosis and treatment of AD.

How glutamatergic synapse loss affects the firing rhythm of DG-CA3 model related with Alzheimer's disease.

As well known that synapse loss is a significant pathological feature of Alzheimer's disease (AD), meanwhile, the hippocampus is one of brain regions to be first affected in the early stage of AD. Thus, this work employs a comprehensive DG-CA3 network model of the hippocampus so as to explore the neuronal correlation between glutamatergic synapse loss and abnormal firing rhythm associated with AD from the perspective of neurocomputation. The neuropathological condition of glutamatergic synapse loss caused by the reduction of Shank3 protein in AD patients is imitated by decreasing glutamatergic excitatory synapse strength between different neurons. By means of power spectral analysis and dynamics technique, the numerical results reveal that excitability of pyramidal neuron as well as oriens lacunosum-moleculare (O-LM) cell in CA3 region is strongly degraded by the decrease of NMDA or AMPA-type glutamatergic excitatory synapse strength. Moreover, the relative power together with the peak of relative power density within alpha band is also diminished by decreasing glutamatergic synapse strength. These findings accord with the electrophysiological experiment of EEG that there is a decrease of alpha rhythm for AD patients, on the same time, they could highlight the significance of glutamatergic synapse loss in the pathogenesis of AD.

Generating and enhancing lag synchronization of chaotic systems by white noise.

In this paper, we study the crucial impact of white noise on lag synchronous regime in a pair of time-delay unidirectionally coupled systems. Our result demonstrates that merely via white-noise-based coupling lag synchronization could be achieved between the coupled systems (chaotic or not). And it is also demonstrated that a conventional lag synchronous regime can be enhanced by white noise. Sufficient conditions are further proved mathematically for noise-inducing and noise-enhancing lag synchronization, respectively. Additionally, the influence of parameter mismatch on the proposed lag synchronous regime is studied, by which we announce the robustness and validity of the new strategy. Two numerical examples are provided to illustrate the validity and some possible applications of the theoretical result.

Controlling Alzheimer's Disease Through the Deep Brain Stimulation to Thalamic Relay Cells.

Experimental and clinical studies have shown that the technique of deep brain stimulation (DBS) plays a potential role in the regulation of Alzheimer's disease (AD), yet it still desires for ongoing studies including clinical trials, theoretical approach and action mechanism. In this work, we develop a modified thalamo-cortico-thalamic (TCT) model associated with AD to explore the therapeutic effects of DBS on AD from the perspective of neurocomputation. First, the neuropathological state of AD resulting from synapse loss is mimicked by decreasing the synaptic connectivity strength from the Inter-Neurons (IN) neuron population to the Thalamic Relay Cells (TRC) neuron population. Under such AD condition, a specific deep brain stimulation voltage is then implanted into the neural nucleus of TRC in this TCT model. The symptom of AD is found significantly relieved by means of power spectrum analysis and nonlinear dynamical analysis. Furthermore, the therapeutic effects of DBS on AD are systematically examined in different parameter space of DBS. The results demonstrate that the controlling effect of DBS on AD can be efficient by appropriately tuning the key parameters of DBS including amplitude A, period P and duration D. This work highlights the critical role of thalamus stimulation for brain disease, and provides a theoretical basis for future experimental and clinical studies in treating AD.

Predicting amplitude death with machine learning.

In nonlinear dynamics, a parameter drift can lead to a sudden and complete cessation of the oscillations of the state variables-the phenomenon of amplitude death. The underlying bifurcation is one at which the system settles into a steady state from chaotic or regular oscillations. As the normal functioning of many physical, biological, and physiological systems hinges on oscillations, amplitude death is undesired. To predict amplitude death in advance of its occurrence based solely on oscillatory time series collected while the system still functions normally is a challenge problem. We exploit machine learning to meet this challenge. In particular, we develop the scheme of "parameter-aware" reservoir computing, where training is conducted for a small number of bifurcation parameter values in the oscillatory regime to enable prediction upon a parameter drift into the regime of amplitude death. We demonstrate successful prediction of amplitude death for three prototypical dynamical systems in which the transition to death is preceded by either chaotic or regular oscillations. Because of the completely data-driven nature of the prediction framework, potential applications to real-world systems can be anticipated.