Restoration of rhythmicity in diffusively coupled dynamical networks

Zou, Wei; Senthilkumar, D. V.; Nagao, Raphael; Kiss, István Z.; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jüergen

doi:10.1038/ncomms8709

Cited by 139 publications

(84 citation statements)

References 70 publications

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“…For example, the low degree nodes are the key nodes that influence the dynamic robustness, while structural robustness is largely influenced by hubs [114]. Note that some dynamic systems can spontaneously recover after a breakdown [39,[107][108][109][110]115,116].…”

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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“…Diffusive coupling is by convention coupling via a term proportional to the state difference between the coupled nodes, that is additive to the individual node dynamics; see, e.g., [24][25][26][27][28][29][30]. Two settings that are based on, in some sense, similar couplings to what we consider here were previously investigated in the superthreshold regime: A first example demonstrated complex behavior as a function of the system parameters, in particular, regarding amplitude death [29], whereas a second example exhibited the crucial role of the coupling for the synchronization between self-sustained circadian oscillator neurons in the suprachiasmatic nucleus of mammals [31]. How then does signal coupling affect the subthreshold behavior of Hopf systems?…”

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confidence: 99%

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

2016

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Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale invariance, from a general level, applicable to all dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., neuronal Hodgkin-Huxley equations). When subject to natural "signal coupling," ensembles of Hopf systems below the bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs at parameter values substantially below where the average of the individual systems would bifurcate, with a frequency profile that is sharpened if compared to the individual systems.

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“…Only recently a general technique to revive oscillation from the oscillation suppressed state (or death state) has been reported by Zou et al [15]. The authors proposed a simple but effective way to revoke the death state and induce rhythmicity by introducing a simple feedback factor in the diffusive coupling.…”

Section: Introductionmentioning

confidence: 99%

“…Any values in between this limit can be treated as the intermediate diffusion rate and thus represent a modified mean-field diffusive coupling. The origin of α is well discussed in [15] where it is speculated that it may arise in the context of cell cycle, neural network and synchronization engineering.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, unlike Ref. [15], here we have two control parameters that enable us to revoke the death state. Using rigorous eigenvalue and bifurcation analyses on coupled van der Pol and Stuart-Landau oscillators, separately, we show that the region of the death state shrinks substantially in the parameter space depending upon those two control parameters.…”

Section: Introductionmentioning

confidence: 99%

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Revival of oscillation from mean-field-induced death: Theory and experiment

2015

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The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in [Zou et al. Nature Commun. 6:7709, 2015], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean-field is capable of inducing rhythmicity even in the presence of complete diffusion, which is an unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the first experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.

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Restoration of rhythmicity in diffusively coupled dynamical networks

Cited by 139 publications

References 70 publications

Recent Progress on the Resilience of Complex Networks

Recent Progress on the Resilience of Complex Networks

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

Revival of oscillation from mean-field-induced death: Theory and experiment

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