Related papers: Emergence of complex structures from nonlinear int…
This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as $k$--dimensional bit--strings.…
In this paper, we study a class of equations representing nonlinear diffusion on networks. A particular instance of our model can be seen as a network equivalent of the porous-medium equation. We are interested in studying perturbations of…
Opinion polarization is a ubiquitous phenomenon in opinion dynamics. In contrast to the traditional consensus oriented group decision making (GDM) framework, this paper proposes a framework with the co-evolution of both opinions and…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate…
The description of large temporal graphs requires effective methods giving an appropriate mesoscopic partition. Many approaches exist today to detect communities in static graphs. However, many networks are intrinsically dynamical, and need…
We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population…
We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are…
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…
This paper establishes a theoretical framework to describe the transition from consensus to stable clustering in multi-agent systems with nonlinear, cooperative interactions. We first establish a sharp threshold for consensus. For a broad…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions $\{0,1\}$ form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can…
Diverse communities of competing species are generally characterized by substantial niche overlap and strongly stochastic dynamics. Abundance fluctuations are proportional to population size, so the dynamics of rare populations is slower.…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
Ecologists have put forward many explanations for coexistence, but these are only partial explanations; nature is complex, so it is reasonable to assume that in any given ecological community, multiple mechanisms of coexistence are…
We consider the process of reaching the final state in the coevolving voter model. There is a coevolution of state dynamics, where a node can copy a state from a random neighbor with probabilty $1-p$ and link dynamics, where a node can…
Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…