I aim to give the flavour of a selection of topics based around Fräıssé’s notion of homogeneous structure. This is an area connecting ideas from model theory, permutation group theory, combinatorics, descriptive set theory, complexity theory, and other subjects. I will touch superficially a number of these subjects, with little in depth. The background assumed will be basic first order logic (l...

For the purposes of this paper, a geometry will consist of a set together with a closure operation on that set, satisfying the exchange condition, and under which singletons are closed (for more precise definitions, see §2.1). The geometry is homogeneous if in the automorphism group of the geometry, the pointwise stabilizer of any finitedimensional closed subset of the geometry is transitive on...

In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spati...