We consider simple mathematical models for the early population dynamics of the human immunodefficiency type 1 virus (HIV-1). Although these systems of differential equations may be solved by numerical methods, few general theoretical results are available due to nonlinearities. We analyze a model whose components are plasma densities of uninfected CD4+ T-cells and infected cells (assumed in th...

Abstract. We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For symmetric increments, the system at long times settles to the Gibbs equilibrium state, while for asymmetric updates, the steady state is out of equilibr...

Bewley considers a dynamic general equilibrium model with heterogeneous consumers. Assuming that the future is sufficiently important, he shows that an equilibrium path converges to a limit which depends upon initial conditions. This study shows that the limit lies near the stationary state independent of initial conditions. This state is the economy’s so-called turnpike ~ a turnpike is usually...