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This paper investigates the problem of fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects. Synchronizing impulses and desynchronizing impulses are each taken into account. The innovative pure power-law control is designed in this paper to avoid vibratory behaviors, which is more straightforward and effective than the common design including the linear and power-law terms. Note that the key difficulty is determining how to ensure fixed-time synchronization and estimate the settling time in an impulsive sense since the impulsive influences may lead to the discontinuity of the states. However, the theoretical framework of fixed-time synchronization under desynchronizing impulses has not been constructed much in the existing literature, which deeply motivated us to contribute to this analysis. By using the average impulsive intervals method, graph theory, and the Lyapunov method, two cases of the settling time along with the fixed-time synchronization criteria regarding the synchronizing and desynchronizing impulses are given. Lastly, a numerical example is provided to show the viability and accuracy of the discovered theoretical results. [ABSTRACT FROM AUTHOR]

Background: Parkinson's disease (PD) has been regarded as a disconnection syndrome with functional and structural disturbances. However, as the anatomic determinants, the structural disconnections in PD have yet to be fully elucidated. Purpose: To non-invasively construct structural networks based on microstructural complexity and to further investigate their potential topological abnormalities in PD given the technical superiority of diffusion kurtosis imaging (DKI) to the quantification of microstructure. Material and Methods: The microstructural data of gray matter in both the PD group and the healthy control (HC) group were acquired using DKI. The structural networks were constructed at the group level by a covariation approach, followed by the calculation of topological properties based on graph theory and statistical comparisons between groups. Results: A total of 51 patients with PD and 50 HCs were enrolled. Individuals were matched between groups with respect to demographic characteristics (P >0.05). The constructed structural networks in both the PD and HC groups featured small-world properties. In comparison with the HC group, the PD group exhibited significantly altered global properties, with higher normalized characteristic path lengths, clustering coefficients, local efficiency values, and characteristic path lengths and lower global efficiency values (P <0.05). In terms of nodal centralities, extensive nodal disruptions were observed in patients with PD (P <0.05); these disruptions were mainly distributed in the sensorimotor network, default mode network, frontal-parietal network, visual network, and subcortical network. Conclusion: These findings contribute to the technical application of DKI and the elucidation of disconnection syndrome in PD. [ABSTRACT FROM AUTHOR]

Aims: This study aimed to characterize the topological alterations and classification performance of high‐order functional connectivity (HOFC) networks in cognitively preserved patients with Parkinson's disease (PD), relative to low‐order FC (LOFC) networks. Methods: The topological metrics of the constructed networks (LOFC and HOFC) obtained from fifty‐one cognitively normal patients with PD and 60 matched healthy control subjects were analyzed. The discriminative abilities were evaluated using machine learning approach. Results: The HOFC networks in the PD group showed decreased segregation and integration. The normalized clustering coefficient and small‐worldness in the HOFC networks were correlated to motor performance. The altered nodal centralities (distributed in the precuneus, putamen, lingual gyrus, supramarginal gyrus, motor area, postcentral gyrus and inferior occipital gyrus) and intermodular FC (frontoparietal and visual networks, sensorimotor and subcortical networks) were specific to HOFC networks. Several highly connected nodes (thalamus, paracentral lobule, calcarine fissure and precuneus) and improved classification performance were found based on HOFC profiles. Conclusion: This study identified disrupted topology of functional interactions at a high level with extensive alterations in topological properties and improved differentiation ability in patients with PD prior to clinical symptoms of cognitive impairment, providing complementary insights into complex neurodegeneration in PD. [ABSTRACT FROM AUTHOR]

The paper is devoted to investigating the quasi-synchronization issue of fractional-order multi-layer networks with mismatched parameters under delay-dependent impulsive feedback control. It is worth highlighting that fractional-order multi-layer networks with mismatched parameters, as the extension model for single-layer or two-layer ones, are constructed in this paper. Simultaneously, the intra-layer and inter-layer couplings are taken into consideration, which is more general and rarely considered in discussions of network synchronization. An extended fractional differential inequality with impulsive effects is given to establish the grounded framework and theory on the quasi-synchronization problem under delay-dependent impulsive feedback control. Moreover, in the light of the Lyapunov method and graph theory, two criteria for achieving the quasi-synchronization of fractional-order multi-layer networks with mismatched parameters are derived. Furthermore, exponential convergence rates as well as the bounds of quasi-synchronization errors are successfully deduced. Ultimately, the theoretical results are applied in a practical power system, and some illustrative examples are proposed to show the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the issue of exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms is investigated by using periodically intermittent control. It deserves to mention that spatial diffusions, multilayer interactions and fractional dynamics are introduced to coupled neural networks at the same time. A novel fractional-order differential inequality is established on the basis of Caputo partial fractional operator. Moreover, to realize exponential synchronization of the underlying neural networks, some sufficient conditions are presented with the help of Lyapunov method and graph theory. Theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. Finally, an illustrative numerical example is provided to further verify the feasibility and effectiveness of our results. [ABSTRACT FROM AUTHOR]

The topic of synchronization of fractional-order fuzzy complex networks with time-varying couplings and proportional delay is addressed in this paper. By combining graph theory, the Lyapunov method, and the Razumikhin method, the synchronization criteria are obtained by designing a new time-varying graph-theoretical Lyapunov function. Different from the typical quadratic Lyapunov function, the time-varying graph-theoretical Lyapunov function contains the product of three-term functions and poses the difficulty of fractional derivative due to the unavailability of the general Leibniz formula and the chain rule. A new inequality about the fractional derivative rule of the time-varying graph-theoretical Lyapunov function is established based on the convex function creatively. In addition, compared with relevant literatures, the synchronization criteria are related to the proportionality coefficient and the order of fractional derivative. Then, the synchronization of fractional-order power system established on fuzzy complex networks with time-varying couplings and proportional delay is studied for the first time by applying the feedback control. Lastly, some simulations are exhibited to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]