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The fluctuating dynamics of a network about its stable, noise-free steady state are theoretically investigated. Various causes of non-equilibrium dynamics are identified in terms of the properties and symmetry of the network connections and…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…
This paper studies the emergence of multi-stability and hysteresis in those systems that arise, under positive feedback, starting from monotone systems with well-defined steady-state responses. Such feedback configurations appear routinely…
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…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
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…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Flexible modulation of temporal dynamics in neural sequences underlies many cognitive processes. For instance, we can adaptively change the speed of motor sequences and speech. While such flexibility is influenced by various factors such as…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast…
We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average…
The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans, and the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is challenging,…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
Conventional power system optimization framework is becoming less reliable and efficient due to the stability issues brought by the ever-increasing inverter-interfaced renewable penetration. To ensure system stability during system…
We analyze the stability of synchronized state for coupled nearly identical dynamical systems on networks by deriving an approximate Master Stability Function (MSF). Using this MSF we treat the problem of designing a network having the best…
Consensus, synchronization, formation control, and power grid balance are all examples of virtuous dynamical states that may arise in networks. Here, we focus on how such states can be destabilized from a fundamental perspective; namely, we…
Base station densification is one of the key approaches for delivering high capacity in radio access networks. However, current static deployments are often impractical and financially unsustainable, as they increase both capital and…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
The study of dynamical systems on complex networks is of paramount importance in engineering, given that many natural and artificial systems find a natural embedding on discrete topologies. For instance, power grids, chemical reactors and…