Certifying spatially uniform behavior in reaction-diffusion PDE and compartmental ODE systems

DOI10.1016/j.automatica.2011.01.010zbMath1235.93124arXiv0908.2614OpenAlexW1997741068MaRDI QIDQ665152

Arcak, Murat

Publication date: 5 March 2012

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.2614

zbMATH Keywords

diffusionlinear matrix inequalitiesdistributed systemsreaction networks

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Classical flows, reactions, etc. in chemistry (92E20) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (11)

Some remarks on spatial uniformity of solutions of reaction-diffusion PDEs ⋮ Analytical Singular Value Decomposition for a Class of Stoichiometry Matrices ⋮ Selective pattern formation control: spatial spectrum consensus and Turing instability approach ⋮ Passivity-based synchronization of a class of complex dynamical networks with time-varying delay ⋮ Exponential synchronization of a class of \(N\)-coupled complex partial differential systems with time-varying delay ⋮ Synchronization under space and time-dependent heterogeneities ⋮ Review on contraction analysis and computation of contraction metrics ⋮ Hamiltonian perspective on compartmental reaction-diffusion networks ⋮ Differential dissipativity analysis of reaction-diffusion systems ⋮ Cluster synchronization of diffusively coupled nonlinear systems: a contraction-based approach ⋮ Contraction after small transients

Uses Software

• CVX

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A passivity-based stability criterion for a class of biochemical reaction networks
• The secant condition for instability in biochemical feedback control. I: The role of cooperativity and saturability
• Three types of matrix stability
• Spatial patterns in coupled biochemical oscillators
• On contraction analysis for non-linear systems
• Diffusive coupling, dissipation, and synchronization
• Diagonal stability of a class of cyclic systems and its connection with the secant criterion
• Global Existence for Semilinear Parabolic Systems
• The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
• Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
• Linear Matrix Inequalities in System and Control Theory
• The chemical basis of morphogenesis
• Basic problems in stability and design of switched systems
• Synchronization of Interconnected Systems With Applications to Biochemical Networks: An Input-Output Approach
• A Passivity-Based Approach to Stability of Spatially Distributed Systems With a Cyclic Interconnection Structure
• Oscillations in I/O Monotone Systems Under Negative Feedback
• Pattern formation outside of equilibrium
• Algebraic connectivity of directed graphs

This page was built for publication: Certifying spatially uniform behavior in reaction-diffusion PDE and compartmental ODE systems