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Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…
When interpersonal interactions between individuals are described by the (discrete or continuous) dynamical systems, the interactions are usually assumed to be instantaneous: the rates of change of the actual states of the actors at given…
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
We study a self-consistent approach to introduce higher-order effects in a branching process model of complex contagion on clustered networks. Branching processes operate over an infinite population such that they never circle back and…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs…
The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…
Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
The structure of a network can significantly influence the properties of the dynamical processes which take place on them. While many studies have been devoted to this influence, much less attention has been devoted to the interplay and…
We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…
The work is presented, leading to the universal contact molecular mechanism of phase transitions and other reactions in solid state. The two components of the mechanism - nucleation and interface propagation - are investigated in detail and…
Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication…
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…