We study higher-order percolation phenomena in two interdependent simplicial complexes. Based on the generating function approach, we develop a theoretical framework that provides insights into the percolation dynamics via pairwise or higher-order 2-simplex interactions among individuals. Our findings reveal that higher-order percolation in such structures displays a richer phase transition behavior than that observed in a single simplicial complex or interdependent dyadic networks. We observe both continuous and discontinuous transitions, which occur with either the removal of a small or large fraction of nodes. The initial phase of the transition, triggered by the removal of a small fraction of nodes, is primarily influenced by the density of triangles in each complex. In contrast, the terminal phase of the transition, during which the giant component disappears, is predominantly determined by the strength of interdependence between two complexes.

In this paper, we exploit the idea of virtual ESPRIT (VESPA) to develop a multi-baseline VESPA (MB-VESPA) approach for direction finding. Specially, we define several cumulant matrices to provide ambiguous direction estimates under different baselines. Fine and unambiguous estimation is then obtained by a simple refinement step. Two refine approaches, termed as successive baseline approach and coprime baseline approach, are subsequently introduced. MB-VESPA shares all the advantages of the VESPA. It is simple, closed-form, search-free, and is applicable to irregularly linear array. In addition, it is free of the impact on the sensor gain uncertainties.

双层网络上的社会传播是当前复杂性研究的热点之一.然而已有研究相对简单,无论线下网络还是线上网络往往采用均匀分布,而经验分析表明线上网络大都是非均匀的.基于这一点,本文研究了线下均匀线上非均匀双层网络上的阈值模型,重点考察了两层网络之间的耦合关系对系统鲁棒性的影响.与完全不相关耦合相比,完全正相关耦合在低连通区域削弱了系统的鲁棒性而在高连通区域增强了系统的鲁棒性,完全负相关耦合则起着相反的作用.与均匀网络相比,非均匀网络上的传播受到耦合相关性的影响更大.

The linear threshold model is widely adopted as a classic prototype for studying contagion processes on social networks, where nodes, representing individuals, are assumed to be in one of two states: inactive or active. Each inactive node can be activated via a threshold rule during evolution. Although both contagion mechanisms and network impacts have been well studied, very few studies paid attention on the effect of interacting strengths on the threshold rule. In this paper, a modified linear threshold model on weighted networks is proposed. On one hand, the weight of a link in the network is characterized by a power-law function of the product of endpoint degrees. On the other hand, peer influences on a node incorporate both the number of its active neighbors and associated link weights. The systematic dynamics is explored by the combination of the spin-glass theory and Monte-Carlo algorithm. In analogy to unweighted networks, a global cascade is not triggered in weighted networks when the average degree of nodes is either too small or too large, however, large cascades are realized within an intermediate range, which is referred to as the cascade window. Moreover, two regimes of the power exponent of the weight function are identified in which the system exhibits distinct behaviors: when networks are very sparse, there exist one extreme of the weight exponent making the system susceptible to large cascades; when the networks are relatively dense, on the contrary, there exists the other extreme of the weight exponent causing the system to maintain optimal robustness. All these results demonstrate the importance of both network connectivity and link weights, and offer a sophisticated description of social contagions.

This article develops a new 2-D direction estimation algorithm using parallel arrays that consist of two parallel nested subarrays. The key idea behind the presented algorithm is to use the difference coarray properties embedded in the auto- and cross correlation matrices of the parallel nested arrays to form a direction-of-arrival (DOA) matrix with enhanced degree of freedoms for 2-D angle estimation. The presented algorithm does not require 2-D nonlinear searching or parameter paring processing. Simulation results demonstrate the superiority of the new algorithm.

考虑到个体相互作用的差异以及个体状态的改变与其理性阈值相关,在均匀和非均匀网络上引入了权重概念,构建了舆情传播的阈值模型,利用蒙特卡罗方法模拟了传播动力学,研究了权重对网络鲁棒性的影响.当网络连通度较低时,存在一个最差权重指数,使得网络的鲁棒性最差;当网络连通度较高时,存在一个最优权重指数,使得网络的鲁棒性最好.

This paper is concerned with the synchronization of two delayed chaotic neural networks with a new adaptive feedback controller which includes state coupling control and delayed state coupling control.By constructing a new Lyapunov functional,we obtain a new adaptive synchronization criteria based on the Lyapunov's stability theory,the linear matrix inequality (LMI) technique and the adaptive feedback control technique.An example and its numerical simulation are given to illustrate the effectiveness of the results.

Community networks are a large and important class of networks widely observed in the real world.Nodes within the same community are highly connected,while the connections between different communities are much sparse.In this paper,an evolving community network model is proposed,where the number of nodes,links,and communities increases with time.The degree of nodes are divided into intra-community degree and inter-community degree.The intracommunity degree represents connections to nodes within the same community while the inter-community degree represents connections to nodes in other communities.Based on the preferential attachment,both degree distributions of the resulting network are power-law,which is proved by the analytical calculation.

We study the impact of age on network evolution which couples addition of new nodes and deactivation of old ones. During evolution, each node experiences two stages: active and inactive. The transition from the active state to the inactive one is based on the rank of the node. In this paper, we adopt age as a criterion of ranking, and propose two deactivation models that generalize previous research. In model A, the older active node possesses the higher rank, whereas in model B, the younger active node takes the higher rank. We make a comparative study between the two models through the node-degree distribution.

This paper is concerned with the problem of global robust asymptotical stability of the equilibrium point for bidirectional associative memory (BAM) neural networks. The activation functions are assumed to be neither differentiable nor strict monotonic and the delays are time-varying. Furthermore, based on the approach of linear matrix inequality (LMI), a new inequality and Lyapunov–Krasovskii functional are applied to derive the results of robust asymptotical stability. Also, a simulation example is presented to demonstrate the effectiveness and applicability of our results.

In this paper, the stochastic stabilization problem for stochastic interval Hopfield neural networks with time-varying delays is investigated. Our attention is focused on the design of a robust state feedback controller such that the closed-loop system is robustly exponentially stable in the mean square. The sufficient conditions are proposed to ensure the existence of desired robust controller, which can be obtained by solving a linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of our theory results.

In this paper, stochastic Hopfield neural networks with time-varying delays are investigated based on Lyapunov-krasovskii functional approach and linear matrix inequality(LMI) technique. The proposed criterion is expressed in terms of linear matrix inequality(LMI)and is less conservative than some existing ones and can be effectively solved by Matlab LMI toolbox. A numerical example that confirms the theoretical result is also presented.

Global robust exponential stability problems for Cohen-Grossberg neural networks are investigated in this paper. New sufficient conditions are derived to ensure the global robust exponential stability of the equilibrium point by using a new inequality and linear matrix inequality technique. A numerical example is given to show the effectiveness of the theoretical results.

In this paper, the stochastic stabilization problem for stochastic interval Hop field neural networks with time-varying delays is investigated. Our attention is focused on the design of a robust state feedback controller such that the closed-loop system is robustly exponentially stable in the mean square. The sufficient conditions are proposed to ensure the existence of desired robust controller, which can be obtained by solving a linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of our theory results.

This paper is concerned with uniqueness and global robust stability for the equilibrium point of the interval bidirectional associative memory (BAM) delayed neural networks. By employing linear matrix inequality and Lyapunov functional, a new criterion is proposed for the global robust stability of BAM neural networks. An example is given to show the effectiveness of the present results.

In this paper, a new sufficient criterion is derived for the uniqueness and global robust stability of the equilibrium point for interval Cohen-Grossberg neural networks with time-varying delays. A new inequality technique combined with the Lyapunov functional method and Linear Matrix Inequality (LMI) technique is taken to investigate this problem. The result is computationally efficient, since it is in the form of a LMI. Two examples are also provided to illustrate the effectiveness of our result.

In this paper, we consider the uniqueness and global robust stability of the equilibrium point of the interval Hopfield-type delayed neural networks. A new criteria is derived by using linear matrix inequality and Lyapunov functional and also a numerical example is given to show the effectiveness of the present results.

In this paper, the global robust asymptotic stability for a class of delayed bidirectional associative memory (BAM) neural networks with interval uncertainty is studied. Some less conservative conditions are presented for the BAM neural networks with multiple time-varing delays based on the Lyapunov functional approach. We also give one example to demonstrate the applicability and effectiveness of our results, and compare the results with the previous robust stability results derived in the literature.

In this paper, several novel sufficient criteria are derived for checking the uniqueness and global robust exponential stability of the equilibrium point for interval Cohen-Grossberg neural networks with time-varying delays. A new approach combing the Lyapunov functional with the matrix inequality techniques is taken to investigate this problem. Also, some remarks and two examples are given to show the effectiveness of the proposed results.

In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results.