ReviewJournal of mathematical biology2012
Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review.
Review in Journal of mathematical biology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
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Who cites it
18 citing papers in PubMed.
- How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection.The Journal of animal ecology · 2023Article
- The hybrid bio-robotic swarm as a powerful tool for collective motion research: a perspective.Frontiers in neurorobotics · 2023Article
- Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis.Bulletin of mathematical biology · 2022Article
- Leadership Through Influence: What Mechanisms Allow Leaders to Steer a Swarm?Bulletin of mathematical biology · 2021Article
- Mathematical models for cell migration: a non-local perspective.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Review
- Multi-scale analysis and modelling of collective migration in biological systems.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Article
- Modelling physical limits of migration by a kinetic model with non-local sensing.Journal of mathematical biology · 2020Article
- Kinetic models with non-local sensing determining cell polarization and speed according to independent cues.Journal of mathematical biology · 2020Article
- Correlated random walks inside a cell: actin branching and microtubule dynamics.Journal of mathematical biology · 2019Article
- Counter-propagating wave patterns in a swarm model with memory.Journal of mathematical biology · 2019Article
- The epidemiological models of Karl-Peter Hadeler.Infectious Disease Modelling · 2018Article
- Article
- Direction-dependent interaction rules enrich pattern formation in an individual-based model of collective behavior.PloS one · 2018Article
- Kinetic Models for Topological Nearest-Neighbor Interactions.Journal of statistical physics · 2017Article
- Locust Collective Motion and Its Modeling.PLoS computational biology · 2015Review
- Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation.Journal of mathematical biology · 2015Article
- Quantification of cell co-migration occurrences during cell aggregation on fibroin substrates.Tissue engineering. Part C, Methods · 2014Article
- Controllability in hybrid kinetic equations modeling nonequilibrium multicellular systems.TheScientificWorldJournal · 2013Article
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Abstract
We briefly review hyperbolic and kinetic models for self-organized biological aggregations and traffic-like movement. We begin with the simplest models described by an advection-reaction equation in one spatial dimension. We then increase the complexity of models in steps. To this end, we begin investigating local hyperbolic systems of conservation laws with constant velocity. Next, we proceed to investigate local hyperbolic systems with density-dependent speed, systems that consider population dynamics (i.e., birth and death processes), and nonlocal hyperbolic systems. We conclude by discussing kinetic models in two spatial dimensions and their limiting hyperbolic models. This structural approach allows us to discuss the complexity of the biological problems investigated, and the necessity for deriving complex mathematical models that would explain the observed spatial and spatiotemporal group patterns.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.