Dynamical Robustness of Complex Biological Networks

Tanaka, Gouhei; Morino, Kazuhide; Aihara, Kazuyuki

doi:10.1007/978-4-431-55444-8_2

Cited by 11 publications

(9 citation statements)

References 50 publications

(72 reference statements)

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“…(4) Figure 5(a) shows the bifurcation diagrams of the variables A x , I x that respectively correspond to the active and inactive prey patches in the reduced model (4), where the inactivation ratio p has been considered as the bifurcation parameter with m = 0.07. Here we would like to note that while discussing Fig.…”

Section: (F)mentioning

confidence: 99%

Survivability of a metapopulation under local extinctions

et al. 2017

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A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks.

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confidence: 99%

Survivability of a metapopulation under local extinctions

et al. 2017

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“…We emphasize that such a setting is different from diffusive coupling and has previously, in the context of laser systems, also been referred to as "injective" coupling [24]. 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].…”

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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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“…The numerical and theoretical analyses of the transition points in this study are expected to be applied to various real-world problems where dynamics is important, including how to effectively prevent epidemic spreading on transportation networks [ 46 ], how to stabilize electric power supply on power networks [ 47 ], and how to robustly keep neuronal firing activity on complex biological networks [ 48 ]. These real-world networks typically have degree correlations [ 8 ], and therefore, we need to take into consideration not only degree distributions but also degree correlations for characterizing the network structure.…”

Section: Discussionmentioning

confidence: 99%

Robustness of Oscillatory Behavior in Correlated Networks

et al. 2015

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Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

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Dynamical Robustness of Complex Biological Networks

Cited by 11 publications

References 50 publications

Survivability of a metapopulation under local extinctions

Survivability of a metapopulation under local extinctions

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

Robustness of Oscillatory Behavior in Correlated Networks

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