2005/10/31 by Quang‐Cuong Pham, Quang-Cuong Pham, Jean-Jacques Slotine · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · #Artificial intelligence #Artificial neural network #Computer science #Control theory (sociology) #Convergence (economics) #Dynamical systems theory #Gene Regulatory Network Analysis #Invariant (physics) #Invariant subspace #Linear subspace #Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Physics #Pure mathematics #Simple (philosophy) #Subspace topology #Synchronization (alternating current) #Topology (electrical circuits) #q-bio.NC
paper · pdf · doi:10.1016/j.neunet.2006.07.008
32 pages, 12 figures. More detailed proofs were given in section 2. Section 3.4 on robust synchronization was added
arxiv created 2006/06/01 · openalex publication_date 2006/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms'' interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flow-invariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Robustnesss of stable concurrent synchronization to variations in individual dynamics is also quantified. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.