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Updated: Feb 6, 2026

Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements
Published on: June 25, 2021
Counter-propagating wave patterns in a swarm model with memory
1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA. angelika.manhart@cims.nyu.edu.
Abstract:
Hyperbolic transport-reaction equations are abundant in the description of movement of motile organisms. Here, we focus on a system of four coupled transport-reaction equations that arises from an age-structuring of a species of turning individuals. By modeling how the behavior depends on the time since the last reversal, we introduce a memory effect. The highlight consists of the explicit construction and characterization of counter-propagating traveling waves, patterns which have been observed in bacterial colonies. Stability analysis reveals conditions for the wave formation as well as pulsating-in-time spatially constant solutions.
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