We consider the absolute stability of the disease-free equilibrium of an intra-host Plasmodium falciparum malarial model allowing for antigenic variation within a single species. Antigenic variation can be viewed as an adaptation of the parasite to evade host defence [2]. The model was recently developed in [3-6]. The host's immune response isâ€¦ (More)

From modeling studies it has been known for >10 years that purely inhibitory networks can produce synchronous output given appropriate balances of intrinsic and synaptic parameters. Several experimental studies indicate that synchronous activity produced by inhibitory networks is critical to the production of population rhythms associated with variousâ€¦ (More)

The goal of the article is to establish the contractivity, on the space of normalised positive distributions, of a certain class of Markov operators defined by stochastic kernels. The motivation for this work is the promising use of stationary densities in characterising convergence properties of a certain class of discrete-time random algorithms,â€¦ (More)

We consider a network of three identical neurons with delayed output. The model for such a network is a system of nonlinear delay differential equations, consisting of multiple discrete delays. Our goal in this article is to establish the existence, and to give a detailed account of the linear stability, of synchronous and mirror-reflecting equilibria.