6 research outputs found
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
Early fragmentation in the adaptive voter model on directed networks
We consider voter dynamics on a directed adaptive network with fixed
out-degree distribution. A transition between an active phase and a fragmented
phase is observed. This transition is similar to the undirected case if the
networks are sufficiently dense and have a narrow out-degree distribution.
However, if a significant number of nodes with low out degree is present, then
fragmentation can occur even far below the estimated critical point due to the
formation of self-stabilizing structures that nucleate fragmentation. This
process may be relevant for fragmentation in current political opinion
formation processes.Comment: 9 pages, 8 figures as published in Phys. Rev.
Fragmentation transitions in multi-state voter models
Adaptive models of opinion formation among humans can display a fragmentation
transition, where a social network breaks into disconnected components. Here,
we investigate this transition in a class of models with arbitrary number of
opinions. In contrast to previous work we do not assume that opinions are
equidistant or arranged on a one-dimensional conceptual axis. Our investigation
reveals detailed analytical results on fragmentations in a three-opinion model,
which are confirmed by agent-based simulations. Furthermore, we show that in
certain models the number of opinions can be reduced without affecting the
fragmentation points.Comment: 11 pages, 8 figure
Analytical calculation of fragmentation transitions in adaptive networks
In adaptive networks fragmentation transitions have been observed in which
the network breaks into disconnected components. We present an analytical
approach for calculating the transition point in general adaptive network
models. Using the example of an adaptive voter model, we demonstrate that the
proposed approach yields good agreement with numerical results.Comment: 4 pages, 4 figure
Emergence and persistence of diversity in complex networks
Complex networks are employed as a mathematical description of complex systems in many different fields, ranging from biology to sociology, economy and ecology. Dynamical processes in these systems often display phase transitions, where the dynamics of the system changes qualitatively. In combination with these phase transitions certain components of the system might irretrievably go extinct. In this case, we talk about absorbing transitions. Developing mathematical tools, which allow for an analysis and prediction of the observed phase transitions is crucial for the investigation of complex networks.
In this thesis, we investigate absorbing transitions in dynamical networks, where a certain amount of diversity is lost. In some real-world examples, e.g. in the evolution of human societies or of ecological systems, it is desirable to maintain a high degree of diversity, whereas in others, e.g. in epidemic spreading, the diversity of diseases is worthwhile to confine. An understanding of the underlying mechanisms for emergence and persistence of diversity in complex systems is therefore essential. Within the scope of two different network models, we develop an analytical approach, which can be used to estimate the prerequisites for diversity.
In the first part, we study a model for opinion formation in human societies. In this model, regimes of low diversity and regimes of high diversity are separated by a fragmentation transition, where the network breaks into disconnected components, corresponding to different opinions. We propose an approach for the estimation of the fragmentation point. The approach is based on a linear stability analysis of the fragmented state close to the phase transition and yields much more accurate results compared to conventional methods.
In the second part, we study a model for the formation of complex food webs. We calculate and analyze coexistence conditions for several types of species in ecological communities. To this aim, we employ an approach which involves an iterative stability analysis of the equilibrium with respect to the arrival of a new species. The proposed formalism allows for a direct calculation of coexistence ranges and thus facilitates a systematic analysis of persistence conditions for food webs.
In summary, we present a general mathematical framework for the calculation of absorbing phase transitions in complex networks, which is based on concepts from percolation theory. While the specific implementation of the formalism differs from model to model, the basic principle remains applicable to a wide range of different models