A review of definitions and measures of system resilience

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

http://absimage.aps.org/image/MAR10/MWS_MAR10-2009-001087.pdf

Catastrophic cascade of failures in interdependent networks

In this paper, the fixed-time synchronization control problem of memristive multidirectional associative memory neural networks (MMAMNNs) is considered. Based on the nonlinear and chaos characteristics of memristor, a chaotic model is constructed. And then, utilizing the Lyapunov stability theory, two appropriate controllers are constructed and different activation functions are used. This control method ensures that drive system and response system can achieve synchronization within a fixed time. So, compared with previous studies, it has more practical value. In addition, we present a fixed-time synchronization chaotic encryption method, the chaos characteristic of the model is used to encrypt plaintext, and the decryption of ciphertext is realized based on the synchronization control theories. Finally, several numerical simulations are given to demonstrate the validity of the theories and the chaotic secure communication scheme.

Fixed-time synchronization control of memristive MAM neural networks with mixed delays and application in chaotic secure communication

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a comprehensive understanding of system robustness under this model by (i) deriving an expression for the final system size as a function of the size of initial attacks; (ii) deriving the critical attack size after which system breaks down completely; (iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and (iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load.

/pdf/optimizing-the-robustness-of-electrical-power-systems-2l66ojev9q.pdf

Optimizing the robustness of electrical power systems against cascading failures

As a nature-inspired search algorithm, firefly algorithm (FA) has several control parameters, which may have great effects on its performance. In this study, we investigate the parameter selection and adaptation strategies in a modified firefly algorithm — adaptive firefly algorithm (AdaFa). There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa. AdaFa is validated over widely used benchmark functions, and the numerical experiments and statistical tests yield useful conclusions on the strategies and the parameter selections affecting the performance of AdaFa. When applied to the real-world problem — protein tertiary structure prediction, the results demonstrated improved variants can rebuild the tertiary structure with the average root mean square deviation less than 0.4A and 1.5A from the native constrains with noise free and 10% Gaussian white noise.

/pdf/adaptive-firefly-algorithm-parameter-analysis-and-its-1hulypz9oz.pdf

Adaptive Firefly Algorithm: Parameter Analysis and its Application

The vulnerability to real-life networks against small initial attacks has been one of outstanding challenges in the study of interrelated networks. We study cascading failures in two interrelated networks S and B composed from dependency chains and connectivity links respectively. This work proposes a realistic model for cascading failures based on the redistribution of traffic flow. We study the Barabasi-Albert networks (BA) and Erdős-Renyi graphs (ER) with such structure and found that the efficiency sharply decreases with increasing percentages of the dependency nodes for removing a node randomly. Furthermore, we study the robustness of interrelated traffic networks, especially the subway and bus network in Beijing. By analyzing different attacking strategies, we uncover that the efficiency of the city traffic system has a non-equilibrium phase transition at low capacity of the networks. This explains why the pressure of the traffic overload is relaxed by singly increasing the number of small buses during rush hours. We also found that the increment of some buses may release traffic jam caused by removing a node of the bus network randomly if the damage is limited. However, the efficiencies to transfer people flow will sharper increase when the capacity of the subway network αS> α0.

/pdf/robustness-of-interrelated-traffic-networks-to-cascading-4w5j0gaqo8.pdf

Robustness of Interrelated Traffic Networks to Cascading Failures

Correlation analysis serves as an easy-to-implement estimation approach for the quantification of the interaction or connectivity between different units. Often, pairwise correlations estimated by sliding windows are time-varying (on different window segments) and window size-dependent (on different window sizes). Still, how to choose an appropriate window size remains unclear. This paper offers a framework for studying this fundamental question by observing a critical transition from a chaotic-like state to a nonchaotic state. Specifically, given two time series and a fixed window size, we create a correlation-based series based on nonlinear correlation measurement and sliding windows as an approximation of the time-varying correlations between the original time series. We find that the varying correlations yield a state transition from a chaotic-like state to a nonchaotic state with increasing window size. This window size-dependent transition is analyzed as a universal phenomenon in both model and real-world systems (e.g., climate, financial, and neural systems). More importantly, the transition point provides a quantitative rule for the selection of window sizes. That is, the nonchaotic correlation better allows for many regression-based predictions.

Universal window size-dependent transition of correlations in complex systems.

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

/pdf/fixed-predefined-time-synchronization-of-memristor-based-vx2emefy.pdf

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with filtering-based edge sampling being the most typical one, heavily relies on an appropriate definition of edge importance. Instead, we propose a different perspective with a generalized local-property-based sampling method, which preserves (scaled) local node characteristics. Apart from degrees, these local node characteristics we use are the expected (scaled) number of wedges and triangles a node belongs to. Through such a preservation, main complex structural properties are preserved implicitly. We adapt a game-theoretic framework from uncertain graph sampling by including a threshold for faster convergence (at least 4 times faster empirically) to approximate solutions. Extensive experimental studies on functional climate networks show the effectiveness of this method in preserving macroscopic to meso-scopic and microscopic network structural properties.

Network Sparsification via Degree- and Subgraph-based Edge Sampling

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyse a model for pendulum clocks coupled by springs and suspended on an oscillating base, and show how EM can be induced in this system by a specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

Zhen Su

Papers

Robustness of Interrelated Traffic Networks to Cascading Failures

Universal window size-dependent transition of correlations in complex systems.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

Network Sparsification via Degree- and Subgraph-based Edge Sampling

Extreme multistability in symmetrically coupled clocks