ReviewFrontiers in network physiology2023
Heteroclinic networks for brain dynamics.
Review in Frontiers in network physiology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
4 citing papers in PubMed.
- Dissimilarity measures for generalized Lotka-Volterra systems on networks.Scientific reports · 2026Article
- Energy landscapes and synergetic state transitions in frustrated Stuart-Landau oscillator networks: a homotopy continuation study.Frontiers in network physiology · 2026Article
- Metastability induced by non-reciprocal adaptive couplings in Kuramoto models.Frontiers in network physiology · 2026Article
- The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives.Frontiers in network physiology · 2023Review
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1 author.
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Abstract
Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka-Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research.
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