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We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with real-valued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where…

Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…

Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing…

A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…

Networks in nature rarely function in isolation but instead interact with one another with a form of a network of networks (NoN). A network of networks with interdependency between distinct networks contains instability of abrupt collapse…

A networked dynamical system is composed of subsystems interconnected through prescribed interactions. In many engineering applications, however, one subsystem can also affect others through "unintended" interactions that can significantly…

Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many body quantum systems, whose underlying lattice structures are generally regular as they're in…

A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…

Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…

Various theoretical and empirical studies have accounted for why humans cooperate in competitive environments. Although prior work has revealed that network structure and multiplex interactions can promote cooperation, most theory assumes…

Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

This work proposes action networks as a semantically well-founded framework for reasoning about actions and change under uncertainty. Action networks add two primitives to probabilistic causal networks: controllable variables and persistent…

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…

Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently…

The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable…

A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among…

Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…