253 research outputs found
Largenet2: an object-oriented programming library for simulating large adaptive networks
The largenet2 C++ library provides an infrastructure for the simulation of
large dynamic and adaptive networks with discrete node and link states. The
library is released as free software. It is available at
http://rincedd.github.com/largenet2. Largenet2 is licensed under the Creative
Commons Attribution-NonCommercial 3.0 Unported License.Comment: 2 pages, 1 figur
Generalized models as a universal approach to the analysis of nonlinear dynamical systems
We present a universal approach to the investigation of the dynamics in
generalized models. In these models the processes that are taken into account
are not restricted to specific functional forms. Therefore a single generalized
models can describe a class of systems which share a similar structure. Despite
this generality, the proposed approach allows us to study the dynamical
properties of generalized models efficiently in the framework of local
bifurcation theory. The approach is based on a normalization procedure that is
used to identify natural parameters of the system. The Jacobian in a steady
state is then derived as a function of these parameters. The analytical
computation of local bifurcations using computer algebra reveals conditions for
the local asymptotic stability of steady states and provides certain insights
on the global dynamics of the system. The proposed approach yields a close
connection between modelling and nonlinear dynamics. We illustrate the
investigation of generalized models by considering examples from three
different disciplines of science: a socio-economic model of dynastic cycles in
china, a model for a coupled laser system and a general ecological food web.Comment: 15 pages, 2 figures, (Fig. 2 in color
Persistence of complex food webs in metacommunities
Metacommunity theory is considered a promising approach for explaining
species diversity and food web complexity. Recently Pillai et al. proposed a
simple modeling framework for the dynamics of food webs at the metacommunity
level. Here, we employ this framework to compute general conditions for the
persistence of complex food webs in metacommunities. The persistence conditions
found depend on the connectivity of the resource patches and the structure of
the assembled food web, thus linking the underlying spatial patch-network and
the species interaction network. We find that the persistence of omnivores is
more likely when it is feeding on (a) prey on low trophic levels, and (b) prey
on similar trophic levels
Robust oscillations in SIS epidemics on adaptive networks: Coarse-graining by automated moment closure
We investigate the dynamics of an epidemiological
susceptible-infected-susceptible (SIS) model on an adaptive network. This model
combines epidemic spreading (dynamics on the network) with rewiring of network
connections (topological evolution of the network). We propose and implement a
computational approach that enables us to study the dynamics of the network
directly on an emergent, coarse-grained level. The approach sidesteps the
derivation of closed low-dimensional approximations. Our investigations reveal
that global coupling, which enters through the awareness of the population to
the disease, can result in robust large-amplitude oscillations of the state and
topology of the network.Comment: revised version 6 pages, 4 figure
Early warning signs for saddle-escape transitions in complex networks
Many real world systems are at risk of undergoing critical transitions,
leading to sudden qualitative and sometimes irreversible regime shifts. The
development of early warning signals is recognized as a major challenge. Recent
progress builds on a mathematical framework in which a real-world system is
described by a low-dimensional equation system with a small number of key
variables, where the critical transition often corresponds to a bifurcation.
Here we show that in high-dimensional systems, containing many variables, we
frequently encounter an additional non-bifurcative saddle-type mechanism
leading to critical transitions. This generic class of transitions has been
missed in the search for early-warnings up to now. In fact, the saddle-type
mechanism also applies to low-dimensional systems with saddle-dynamics. Near a
saddle a system moves slowly and the state may be perceived as stable over
substantial time periods. We develop an early warning sign for the saddle-type
transition. We illustrate our results in two network models and epidemiological
data. This work thus establishes a connection from critical transitions to
networks and an early warning sign for a new type of critical transition. In
complex models and big data we anticipate that saddle-transitions will be
encountered frequently in the future.Comment: revised versio
Adaptive network models of collective decision making in swarming systems
We consider a class of adaptive network models where links can only be
created or deleted between nodes in different states. These models provide an
approximate description of a set of systems where nodes represent agents moving
in physical or abstract space, the state of each node represents the agent's
heading direction, and links indicate mutual awareness. We show analytically
that the adaptive network description captures the phase transition to
collective motion in swarming systems and that the properties of this
transition are determined by the number of states (discrete heading directions)
that can be accessed by each agent.Comment: 8 pages, 5 figure
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