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Abrupt transitions in ecosystems can be interconnected, raising challenges for science and management in identifying sufficient interventions to prevent them or recover from undesirable shifts. Here we use principles of network…

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…

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…

Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a…

Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

We introduce an approach to partitioning networks into communities that not only determines the best community structure, but also provides a range of characterization techniques to assess how significant that structure is. We study the…

We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…

[Background] Several studies have mentioned network modularity -- that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other -- as a factor affecting metabolic…

Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…

To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of…

We use the context of dryland vegetation to study a general problem of complex pattern forming systems - multiple pattern-forming instabilities that are driven by distinct mechanisms but share the same spectral properties. We find that the…

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…

A mutualism is an interaction where the involved species benefit from each other. We study a two-dimensional hexagonal three-state cellular automaton model of a two-species mutualistic system. The simple model is characterized by four…

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…

Recent studies suggest that the emergence of cooperative behavior can be explained by generalized reciprocity, a behavioral mechanism based on the principle of "help anyone if helped by someone". In complex systems, the cooperative dynamics…

We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…