mathematical model

The risk of marine bioinvasion caused by global shipping

The rate of biological invasions has strongly increased during the last decades, mostly due to the accelerated spread of species by increasing global trade and transport. Here, we combine the network of global cargo ship movements with port environmental conditions and biogeography to quantify the probability of new primary invasions through the release of ballast water...

A graphical theory of competition on spatial resource gradients

Resource competition is a fundamental interaction in natural communities. However, little remains known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyse the competition of two …

Cycles, phase synchronization, and entrainment in single-species phytoplankton populations

Complex dynamics, such as population cycles, can arise when the individual members of a population become synchronized. However, it is an open question how readily and through which mechanisms synchronization-driven cycles can occur in unstructured …

Zipf’s law in the popularity distribution of chess openings

We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of …

Wave mediated synchronization of nonuniform oscillatory media

We characterize the spatiotemporal evolution of a photosensitive Belousov-Zhabotinsky medium that is made up of coupled oscillatory cells with randomly distributed frequencies. The medium evolves from an initial state of multiple wave sources to a …

Structural kinetic modeling of metabolic networks

To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still …

Epidemic dynamics on an adaptive network

Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by …

Quasiregular concentric waves in heterogeneous lattices of coupled oscillators

We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasiregular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found …

Community response to enrichment is highly sensitive to model structure

Biologists use mathematical functions to model, understand and predict nature. For most biological processes, however, the exact analytical form is not known. This is also true for one of the most basic life processes: the uptake of food or …

Synchronization of two interacting populations of oscillators

We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of …