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Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well-defined internal mechanical motions to various initial deformations and that these…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of information and the transmission machinery induce…
Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such…
In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected…
The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
How biological networks achieve robust control despite relying on imperfect, local information remains an important open question. Here, we identify thermodynamic constraints that can curtail non-equilibrium steady-state responses so…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the…
The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network…