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Spatially extended patterns and multistability of possible different states is common in many ecosystems, and their combination has an important impact on their dynamical behaviours. One potential combination involves tristability between a…
Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
Group formation and coordination are fundamental characteristics of living systems, essential for performing tasks and ensuring survival. Interactions between individuals play a key role in group formation, and the impact of resource…
Modular structure is ubiquitous among real-world networks from related proteins to social groups. Here we analyze the modular organization of brain networks at a large-scale (voxel level) extracted from functional magnetic resonance imaging…
Explaining coexistence in species-rich communities of primary producers remains a challenge for ecologists because of their likely competition for shared resources. Following Hutchinson's seminal suggestion, many theoreticians have tried to…
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here we provide an overview of this rapidly growing…
In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics…
Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
Large-scale online campaigns, malicious or otherwise, require a significant degree of coordination among participants, which sparked interest in the study of coordinated online behavior. State-of-the-art methods for detecting coordinated…
Cooperation is ubiquitous ranging from multicellular organisms to human societies. Population structures indicating individuals' limited interaction ranges are crucial to understand this issue. But it is still at large to what extend…
Active matter systems typically exhibit a trade-off between structural robustness and dynamical freedom, limiting independent control over structure and motion. Here, we show that encoding interactions in a shared field overcomes this…
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…
The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…