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Conservation laws and symmetry in economic growth models: a geometrical approach.

Manuel de León, David Martín de Diego (1998)

Extracta Mathematicae

The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian function...

Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems

Weiyong Yu, Zhenhua Deng, Hongbing Zhou, Xianlin Zeng (2017)

Kybernetika

This paper is concerned with solving the distributed resource allocation optimization problem by multi-agent systems over undirected graphs. The optimization objective function is a sum of local cost functions associated to individual agents, and the optimization variable satisfies a global network resource constraint. The local cost function and the network resource are the private data for each agent, which are not shared with others. A novel gradient-based continuous-time algorithm is proposed...

Inverse Limits, Economics, and Backward Dynamics.

Judy Kennedy (2008)

RACSAM

We survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics.

Mean stability of a stochastic difference equation

Viorica Mariela Ungureanu, Sui Sun Cheng (2008)

Annales Polonici Mathematici

A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...

Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case

Nico M. van Dijk, Karel Sladký (2006)

Kybernetika

In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as generalization of the pure stochastic case, for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II. In the present Part I it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly...

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