English
Related papers

Related papers: Diffusion-dynamics laws in stochastic reaction net…

200 papers

This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…

Analysis of PDEs · Mathematics 2026-05-07 Théo André , Szymon Cygan , Anna Marciniak-Czochra , Finn Münnich

Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…

Discrete Mathematics · Computer Science 2013-07-15 Loïc Paulevé , Gheorghe Craciun , Heinz Koeppl

Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are…

Adaptation and Self-Organizing Systems · Physics 2020-10-21 Zachary G. Nicolaou , Takashi Nishikawa , Schuyler B. Nicholson , Jason R. Green , Adilson E. Motter

We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…

Dynamical Systems · Mathematics 2026-05-07 Dinesh Kumar

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the…

Physics and Society · Physics 2009-11-13 An-Cai Wu , Xin-Jian Xu , J. F. F. Mendes , Ying-Hai Wang

Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g. optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the…

Soft Condensed Matter · Physics 2024-01-24 Henry Alston , Thibault Bertrand

External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and…

Statistical Mechanics · Physics 2024-10-15 Iman Abdoli , Kristian Stølevik Olsen , Hartmut Löwen

Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input…

Molecular Networks · Quantitative Biology 2023-02-03 Yuji Hirono , Hyukpyo Hong , Jae Kyoung Kim

We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…

Statistical Mechanics · Physics 2025-12-02 Olivier Rivoire , Guy Bunin

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…

Neurons and Cognition · Quantitative Biology 2017-05-10 Francesca Mastrogiuseppe , Srdjan Ostojic

Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…

Molecular Networks · Quantitative Biology 2019-04-19 Tan Van Vu , Yoshihiko Hasegawa

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…

Probability · Mathematics 2009-01-27 Carl Mueller , Roger Tribe

The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition…

Statistical Mechanics · Physics 2014-02-04 Xavier Durang , Malte Henkel , Hyunggyu Park

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…

Mathematical Physics · Physics 2023-05-31 Chris D Greenman

We study a stochastic multiscale spatial gene network. These naturally arise in molecular biology. In our model, the reactants are subject to on-site reactions on both scales and diffusion on the continuous scale only, although diffusion on…

Probability · Mathematics 2026-04-01 Arnaud Debussche , Baptiste Huguet

The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this…

Chaotic Dynamics · Physics 2017-02-28 Rafail V. Abramov

We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics…

Probability · Mathematics 2010-02-27 Panayotis Mertikopoulos , Aris L. Moustakas

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The…

Optimization and Control · Mathematics 2015-06-03 Xiaochuan Zhao , Sheng-Yuan Tu , Ali H. Sayed

This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…

Optimization and Control · Mathematics 2025-11-24 Somnath Pradhan , Dinesh Rathia

The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…

Pattern Formation and Solitons · Physics 2025-10-22 Lorenzo Giambagli , Lucille Calmon , Riccardo Muolo , Timoteo Carletti , Ginestra Bianconi