2,001 research outputs found
From neurons to epidemics: How trophic coherence affects spreading processes
Trophic coherence, a measure of the extent to which the nodes of a directed
network are organised in levels, has recently been shown to be closely related
to many structural and dynamical aspects of complex systems, including graph
eigenspectra, the prevalence or absence of feed-back cycles, and linear
stability. Furthermore, non-trivial trophic structures have been observed in
networks of neurons, species, genes, metabolites, cellular signalling,
concatenated words, P2P users, and world trade. Here we consider two simple yet
apparently quite different dynamical models -- one a
Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include
complex contagion, the other an Amari-Hopfield neural network -- and show that
in both cases the related spreading processes are modulated in similar ways by
the trophic coherence of the underlying networks. To do this, we propose a
network assembly model which can generate structures with tunable trophic
coherence, limiting in either perfectly stratified networks or random graphs.
We find that trophic coherence can exert a qualitative change in spreading
behaviour, determining whether a pulse of activity will percolate through the
entire network or remain confined to a subset of nodes, and whether such
activity will quickly die out or endure indefinitely. These results could be
important for our understanding of phenomena such as epidemics, rumours, shocks
to ecosystems, neuronal avalanches, and many other spreading processes
Topological resilience in non-normal networked systems
The network of interactions in complex systems, strongly influences their
resilience, the system capability to resist to external perturbations or
structural damages and to promptly recover thereafter. The phenomenon manifests
itself in different domains, e.g. cascade failures in computer networks or
parasitic species invasion in ecosystems. Understanding the networks
topological features that affect the resilience phenomenon remains a
challenging goal of the design of robust complex systems. We prove that the
non-normality character of the network of interactions amplifies the response
of the system to exogenous disturbances and can drastically change the global
dynamics. We provide an illustrative application to ecology by proposing a
mechanism to mute the Allee effect and eventually a new theory of patterns
formation involving a single diffusing species
Topological resilience in non-normal networked systems
The network of interactions in complex systems, strongly influences their
resilience, the system capability to resist to external perturbations or
structural damages and to promptly recover thereafter. The phenomenon manifests
itself in different domains, e.g. cascade failures in computer networks or
parasitic species invasion in ecosystems. Understanding the networks
topological features that affect the resilience phenomenon remains a
challenging goal of the design of robust complex systems. We prove that the
non-normality character of the network of interactions amplifies the response
of the system to exogenous disturbances and can drastically change the global
dynamics. We provide an illustrative application to ecology by proposing a
mechanism to mute the Allee effect and eventually a new theory of patterns
formation involving a single diffusing species
From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems
The recent discovery of universal principles underlying many complex networks
occurring across a wide range of length scales in the biological world has
spurred physicists in trying to understand such features using techniques from
statistical physics and non-linear dynamics. In this paper, we look at a few
examples of biological networks to see how similar questions can come up in
very different contexts. We review some of our recent work that looks at how
network structure (e.g., its connection topology) can dictate the nature of its
dynamics, and conversely, how dynamical considerations constrain the network
structure. We also see how networks occurring in nature can evolve to modular
configurations as a result of simultaneously trying to satisfy multiple
structural and dynamical constraints. The resulting optimal networks possess
hubs and have heterogeneous degree distribution similar to those seen in
biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of
Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200
Catastrophic regime shifts in model ecological communities are true phase transitions
Ecosystems often undergo abrupt regime shifts in response to gradual external
changes. These shifts are theoretically understood as a regime switch between
alternative stable states of the ecosystem dynamical response to smooth changes
in external conditions. Usual models introduce nonlinearities in the
macroscopic dynamics of the ecosystem that lead to different stable attractors
among which the shift takes place. Here we propose an alternative explanation
of catastrophic regime shifts based on a recent model that pictures ecological
communities as systems in continuous fluctuation, according to certain
transition probabilities, between different micro-states in the phase space of
viable communities. We introduce a spontaneous extinction rate that accounts
for gradual changes in external conditions, and upon variations on this control
parameter the system undergoes a regime shift with similar features to those
previously reported. Under our microscopic viewpoint we recover the main
results obtained in previous theoretical and empirical work (anomalous
variance, hysteresis cycles, trophic cascades). The model predicts a gradual
loss of species in trophic levels from bottom to top near the transition. But
more importantly, the spectral analysis of the transition probability matrix
allows us to rigorously establish that we are observing the fingerprints, in a
finite size system, of a true phase transition driven by background
extinctions.Comment: 19 pages, 11 figures, revised versio
A food chain ecoepidemic model: infection at the bottom trophic level
In this paper we consider a three level food web subject to a disease
affecting the bottom prey. The resulting dynamics is much richer with respect
to the purely demographic model, in that it contains more transcritical
bifurcations, gluing together the various equilibria, as well as persistent
limit cycles, which are shown to be absent in the classical case. Finally,
bistability is discovered among some equilibria, leading to situations in which
the computation of their basins of attraction is relevant for the system
outcome in terms of its biological implications
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