Two-type interacting particles with non-local order-based switching converge in law to a McKean-Vlasov process whose long-time behavior includes traveling waves identified via phase-plane analysis of a reduced ODE system for exponential jumps.
Follow-the-Leader models can be viewed as a numerical approximation to the
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Flocking with Multiple Types: Competition, Fluid Limits and Traveling Waves
Two-type interacting particles with non-local order-based switching converge in law to a McKean-Vlasov process whose long-time behavior includes traveling waves identified via phase-plane analysis of a reduced ODE system for exponential jumps.