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...

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists wit...

Model equations for the description of chemical reactions of dissociation and recombination through a transition state constitute necessarily singular perturbation problems because of the very short lifetime of the excited molecules, compared to all other characteristic times. Asymptotic solutions are derived and tested versus an accurate numerical solution by resorting to different expansion a...

A system of reaction-diffusion differential equations is utilized to model the diffusion of a population through annular patches with different carrying capacities. In the case of continuous solutions with continuous flux, it is shown that a unique, positive steady-state solution exists. In the case of radially symmetric initial conditions, it is shown that all solutions of the Cauchy problem a...

In this paper, we describe our application of SPIN [1] to model an algorithm used to synchronize the clocks of modules that provide periodic real-time communication over a network. We used the SPIN model to check certain performance properties of the system; in particular, we were able to verify that the algorithm achieves synchronization within a time bound, even in the presence of certain typ...

This paper considers a one-sector overlapping-generations model with production. We observe that under standard assumptions on preferences and technology, the perfect-foresight equilibrium violates positivity constraints for large sets of initial conditions. The consideration of the positivity constraints of the consumer enables degenerate equilibrium, a perfect-foresight equilibrium that remai...

We discuss the problem of semi-globally asymptotically stabilizing general nonlinear discretetime systems in the presence of data-rate constraints under the stabilizability assumption only. The proposed solution relies on a simple result on asymptotic estimation for nonlinear systems under data-rate constraints, which holds for trajectories confined within a known bounded region of the state sp...

This paper introduces condition/event (C/E) systems as a class of continuous-time discrete event dynamic systems (DEDS) with two types of discrete-valued input and output signals: condition signals and event signals. In applications such as discrete control, C/E systems provide an intuitive continuous-time modeling framework amenable to block diagram representation. In this paper we consider C/...

The Hoare state monad provides a powerful means of structuring the verification of higher-order, stateful programs. This paper defines a new variant of the Hoare state monad, which, rather than being a triple of a pre-condition, a return type, and a post-condition, is a pair of a return type and a predicate transformer. We dub this monad the Dijkstra state monad. Using the Dijkstra state monad,...

We solve the problem of whether a set of quantum tests reveals state-independent contextuality and use this result to identify the simplest set of the minimal dimension. We also show that identifying state-independent contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112, 040404 (2014)] is not sufficient for revealing state-independent contextuality.