We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted versus repelled by a single chemical substance. The production versus destruction rates of the chemotactic substance by the species is described by a probability measure. For such a model, we investigate the variational structures, in particular, we prove the existence of Lyapunov functionals, we establish duality properties as well as a logarithmic Hardy–Littlewood–Sobolev type inequality for the associated free energy. The latter inequality provides the optimal critical value for the conserved total population mass.
