Dynamical robustness analysis of weighted complex networks

Zhang, He; Liu, Shuai; Zhan, Meng

doi:10.1016/j.physa.2013.05.005

Cited by 41 publications

(23 citation statements)

References 29 publications

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“…For example, the robustness of dynamic traffic networks [35] can be improved by increasing the velocities of the bottleneck links, which are identified via the dynamic functional traffic network. Moreover, the dynamical robustness of complex networks, which is defined as the ability of a network to maintain its dynamical activity, when a fraction of the dynamical components are deteriorated or functionally depressed, but not removed [113], may be different from the structural robustness. For example, the low degree nodes are the key nodes that influence the dynamic robustness, while structural robustness is largely influenced by hubs [114].…”

Section: Discussionmentioning

confidence: 99%

Recent Progress on the Resilience of Complex Networks

Gao

Liu

et al. 2015

Energies

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Many complex systems in the real world can be modeled as complex networks, which has captured in recent years enormous attention from researchers of diverse fields ranging from natural sciences to engineering. The extinction of species in ecosystems and the blackouts of power girds in engineering exhibit the vulnerability of complex networks, investigated by empirical data and analyzed by theoretical models. For studying the resilience of complex networks, three main factors should be focused on: the network structure, the network dynamics and the failure mechanism. In this review, we will introduce recent progress on the resilience of complex networks based on these three aspects. For the network structure, increasing evidence shows that biological and ecological networks are coupled with each other and that diverse critical infrastructures interact with each other, triggering a new research hotspot of "networks of networks" (NON), where a network is formed by interdependent or interconnected networks. The resilience of complex networks is deeply influenced by its interdependence with other networks, which can be analyzed and predicted by percolation theory. This review paper shows that the analytic framework for Energies 2015, 8 12188 NON yields novel percolation laws for n interdependent networks and also shows that the percolation theory of a single network studied extensively in physics and mathematics in the last 60 years is a specific limited case of the more general case of n interacting networks. Due to spatial constraints inherent in critical infrastructures, including the power gird, we also review the progress on the study of spatially-embedded interdependent networks, exhibiting extreme vulnerabilities compared to their non-embedded counterparts, especially in the case of localized attack. For the network dynamics, we illustrate the percolation framework and methods using an example of a real transportation system, where the analysis based on network dynamics is significantly different from the structural static analysis. For the failure mechanism, we here review recent progress on the spontaneous recovery after network collapse. These findings can help us to understand, realize and hopefully mitigate the increasing risk in the resilience of complex networks.

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Section: Discussionmentioning

confidence: 99%

Recent Progress on the Resilience of Complex Networks

Gao

Liu

et al. 2015

Energies

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“…The property related to robustness and fragility of the heterogeneously coupled networks can be altered for another type of coupling [39]. An example of the model with weighted coupling is described as follows:…”

Section: Weighted Couplingmentioning

confidence: 99%

Dynamical Robustness of Complex Biological Networks

Tanaka

Morino

Aihara

2015

Mathematical Approaches to Biological Systems

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Dynamical behavior of biological systems is maintained by interactions between biological units such as neurons, cells, proteins, and molecules. It is a challenging issue to understand robustness of biological interaction networks from a viewpoint of dynamical systems. In this chapter, we introduce the concept of dynamical robustness in complex networks and demonstrate its application to biological networks. First, we introduce the framework for studying the dynamical robustness through analyses of coupled Stuart-Landau oscillators with various types of network structures. Second, based on the framework, we examine the dynamical robustness of neuronal firing activity in networks of synaptically coupled MorrisLecar neuron models. Our analyses suggest that a consideration of both network structure and dynamics is crucial in elucidating biological robustness.

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“…By setting M = 2, p 1 = 1 − p, p 2 = p, a 1 = a > 0, and a 2 = −b < 0 and solving Eq. (14) with respect to p, we can derive the critical point for the globally coupled network with d j 1 as [7] and that for more complex networks as [13]. Now, let us examine the effect of population heterogeneity on the critical threshold in the oscillator networks where the control parameter values are continuously distributed.…”

Section: B Derivation Of the Critical Pointmentioning

confidence: 99%

“…In all the cases, an increase in the standard deviation σ of the distribution of α j results in the almost monotonic decrease in the critical value μ c . Next, we consider the following oscillator network model with weighted coupling [14]:…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…This phenomenon is called an aging transition [7]. The critical fraction p c has been examined for various types of networks, including globally coupled networks [7][8][9][10], locally coupled networks [11], multilayered networks [12], and complex networks [13,14]. Since a larger value of p c implies that the global oscillation is more tolerant to inactivation of the oscillators, p c can be used as a measure for evaluating dynamical robustness of oscillator networks [7].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical robustness of coupled heterogeneous oscillators

et al. 2014

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We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.

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Dynamical robustness analysis of weighted complex networks

Cited by 41 publications

References 29 publications

Recent Progress on the Resilience of Complex Networks

Recent Progress on the Resilience of Complex Networks

Dynamical Robustness of Complex Biological Networks

Dynamical robustness of coupled heterogeneous oscillators

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