相关论文: Endotactic Networks and Toric Differential Inclusi…

In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the structure of the underlying network through Lyapunov functions…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…

All types of networks arise as intricate combinations of dyadic building blocks formed by pairs of vertices. In directed networks, the dyadic patterns are entirely determined by reciprocity, i.e. the tendency to form, or to avoid, mutual…

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct…

Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so…

Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…

When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…

Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…

Persistency is the property, for differential equations in $\R^n$, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction property:…

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…

Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…

The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the…

We investigate the relationship between the nested organization of mutualistic systems and their robustness against the extinction of species. We establish that a nested pattern of contacts is the best possible one as far as robustness is…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…

The robustness of an ecological network quantifies the resilience of the ecosystem it represents to species loss. It corresponds to the proportion of species that are disconnected from the rest of the network when extinctions occur…

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems…