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Chase-and-run and chirality in nonlocal models of pattern formation

Abstract:
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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Publisher copy:
10.1007/s11538-025-01539-6

Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8257-4910
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St John's College
Role:
Author
ORCID:
0000-0002-0146-9164
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-6888-4362


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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:
1522-9602
ISSN:
0092-8240


Language:
English
Keywords:
Pubs id:
2300378
Local pid:
pubs:2300378
Deposit date:
2025-10-19
ARK identifier:

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