相关论文: The Samuelson's model as a singular discrete time …

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…

We introduce an integrable time-discretized version of the classical Calogero-Moser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the…

This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and…

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus…

This is a short letter summarizing the long paper cond-mat/0106047 in which we present a simple two-dimensional dynamical system reaching a singularity in finite time decorated by accelerating oscillations due to the interplay between…

A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…

The mathematical model proposed by George Soros for his theory of reflexivity is analyzed under the framework of discrete dynamical systems. We show the importance of the notion of fixed points for explaining the behavior of a reflexive…

A common approach to analyze count time series is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a…

This paper presents SIMPOL (Simplified Policy Iteration), a modular numerical framework for solving continuous-time heterogeneous agent models. The core economic problem, the optimization of consumption and savings under idiosyncratic…

We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…

This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously,…

Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…

This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…

We study discrete-time $(m,n)$-multirate systems on separable Hilbert spaces, solving the problem of approximating such a system by one which has a shorter multirate period $(m/q,n/q)$, optimally in the Hilbert-Schmidt norm. We work in the…

We study in this work the concept of instantaneous time mirrors that were recently introduced in the physics literature. Instantaneous time mirrors offer a new method for time reversal with a simplified experimental setup compared to…

We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…

Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…

In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm…