Journal article
Chase-and-run and chirality in nonlocal models of pattern formation
- Abstract:
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Chase-and-run dynamics, in which one population pursues another that flees from it, are found throughout nature, from predator-prey interactions in ecosystems to the collective motion of cells during development. Intriguingly, in many of these systems, the movement is not straight; instead, ‘runners’ veer off at an angle from their pursuers. This angled movement often exhibits a consistent left–right asymmetry, known as lateralisation or chirality. Inspired by such phenomena in zebrafish skin patterns and evasive animal motion, we explore how chirality shapes the emergence of patterns in nonlocal (integro-differential) advection-diffusion models. We extend such models to allow movement at arbitrary angles, uncovering a rich landscape of behaviours. We find that chirality can enhance pattern formation, suppress oscillations, and give rise to entirely new dynamical structures, such as rotating pulses of chasers and runners. We also uncover how chase-and-run dynamics can cause populations to mix or separate. Through linear stability analysis, we identify physical mechanisms that drive some of these effects, whilst also exposing striking limitations of this theory in capturing more complex dynamics. Our findings suggest that chirality could have roles in ecological and cellular patterning beyond simply breaking left-right symmetry.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 2.1MB, Terms of use)
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- Publisher copy:
- 10.1007/s11538-025-01539-6
Authors
+ Engineering and Physical Sciences Research Council
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- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- EP/W524311/1
- Publisher:
- Springer Nature
- Journal:
- Bulletin of Mathematical Biology More from this journal
- Volume:
- 87
- Issue:
- 11
- Article number:
- 160
- Publication date:
- 2025-10-14
- Acceptance date:
- 2025-09-27
- DOI:
- EISSN:
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1522-9602
- ISSN:
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0092-8240
- Language:
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English
- Keywords:
- Pubs id:
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2300378
- Local pid:
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pubs:2300378
- Deposit date:
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2025-10-19
- ARK identifier:
Terms of use
- Copyright holder:
- Jewell et al
- Copyright date:
- 2025
- Rights statement:
- © The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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