Related papers: Dynamic and static limitation in multiscale reacti…
We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods for proving hypocoercivity of the linearized equations. Exponential decay of…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…
We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this…
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction…
Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Elastic structures can be designed to exhibit precise, complex, and exotic functions. While recent work has focused on the quasistatic limit governed by force balance, the mechanics at a finite driving rate are governed by Newton's…
Recurrent neural network-based reinforcement learning systems are capable of complex motor control tasks such as locomotion and manipulation, however, much of their underlying mechanisms still remain difficult to interpret. Our aim is to…
The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirected networks of nonlinear dynamical systems, when we consider…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…
We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output…
Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically…