2014/04/07 by Pietro De Lellis, Pietro DeLellis, DeLellis, Pietro +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #93A14 #Algorithm #Applied mathematics #Bounded function #Combinatorics #Computer science #Convergence (economics) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Lyapunov function #Mathematical analysis #Mathematical optimization #Mathematics #Neural Networks Stability and Synchronization #Node (physics) #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Piecewise #Set (abstract data type) #State (computer science) #Synchronization (alternating current) #Topology (electrical circuits) #Upper and lower bounds #math.DS #msc:93A14
paper · pdf · doi:10.48550/arxiv.1404.1835
published in arXiv (Cornell University) (Cornell University) · 50 pages, 11 figures
arxiv created 2014/04/07 · openalex publication_date 2014/04/07 · arxiv updated 2014/04/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/05
This paper presents a framework for the study of convergence when the nodes'\ndynamics may be both piecewise smooth and/or nonidentical across the network.\nSpecifically, we derive sufficient conditions for global convergence of all\nnode trajectories towards the same bounded region of their state space. The\nanalysis is based on the use of set-valued Lyapunov functions and bounds are\nderived on the minimum coupling strength required to make all nodes in the\nnetwork converge towards each other. We also provide an estimate of the\nasymptotic bound \ε on the mismatch between the node states at steady\nstate. The analysis is performed both for linear and nonlinear coupling\nprotocols. The theoretical analysis is extensively illustrated and validated\nvia its application to a set of representative numerical examples.\n