Related papers: Collective Behavior and Memory States in Flow Netw…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
The asymmetry model for the highly viscous flow postulates thermally activated jumps from a practically undistorted ground state to strongly distorted, but stable structures, with a pronounced Eshelby backstress from the distorted…
Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient…
The past few years have seen great strides in our ability to build synthetic microscopic machines. However, the function of such machines is often controlled directly by externally applied fields that deterministically specify the…
We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra…
Understanding the interactions among nodes in a complex network is of great importance, since they disclose how these nodes are cooperatively supporting the functioning of the network. Scientists have developed numerous methods to uncover…
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
Growing evidence suggests that the macroscopic functional states of urban road networks exhibit multistability and hysteresis, but microscopic mechanisms underlying these phenomena remain elusive. Here, we demonstrate that in real-world…
Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study, by using liquid-state theories and Monte Carlo simulation, the behavior of systems of classical particles interacting through a finite pair repulsion supplemented with a longer range attraction. Any such potential can be driven…
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and…
We prove that complex networks of interactions have the capacity to regulate and buffer unpredictable fluctuations in production events. We show that non-bursty network-driven activation dynamics can effectively regulate the level of…
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can generate sequences of metastable cluster states where each…
Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of…
Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying…
A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of…