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This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…
Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…
Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In presence of triadic interactions, a percolation process occurring on a…
The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, we show that there are certain mesoscale subgraphs…
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…
We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…