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This paper deals with analysis and numerical simulations of a one-dimensionaltwo-species hyperbolic aggregation model. This model is formed by a system oftransport equations with nonlocal velocities, which describes the aggregatedynamics of a two-species population in interaction appearing for instance inbacterial chemotaxis. Blow-up of classical solutions occurs in finite time.This raises the question to define measure-valued solutions for this system. Tothis aim, we use the duality method developed for transport equations withdiscontinuous velocity to prove the existence and uniqueness of measure-valuedsolutions. The proof relies on a stability result. In addition, this approachallows to study the hyperbolic limit of a kinetic chemotaxis model. Moreover,we propose a finite volume numerical scheme whose convergence towardsmeasure-valued solutions is proved. It allows for numerical simulationscapturing the behaviour after blow up. Finally, numerical simulationsillustrate the complex dynamics of aggregates until the formation of a singleaggregate: after blow-up of classical solutions, aggregates of differentspecies are synchronising or nonsynchronising when collide, that is movetogether or separately, depending on the parameters of the model and masses ofspecies involved.

Synchronising and Non-synchronising Dynamics for a Two-species Aggregation Model