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We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…
In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving…
We furnish necessary and sufficient conditions for the occurrence of a Hopf bifurcation in a particularly significant fluid-structure problem, where a Navier-Stokes liquid interacts with a rigid body that is subject to an undamped elastic…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…
We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…
Often exhibiting hierarchical and overlapping structures, communities or modular groups are fundamental and complex in network science. One of the most exploited tools to detect the mesoscopic structure is synchronization. Several phenomena…
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily…
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…
Understanding how opinions spread through a community or how consensus emerges in noisy environments can have a significant impact on our comprehension of social relations among individuals. In this work a model for the dynamics of opinion…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
We introduce a model for the formation of social networks, which takes into account the homophily or the tendency of individuals to associate and bond with similar others, and the mechanisms of global and local attachment as well as tie…
We study the emergent dynamics of a network of synaptically coupled slow-fast oscillators. Synaptic coupling provides a network-level positive feedback mechanism that cooperates with cellular-level positive feedback to ignite in-phase…