Related papers: Mathematical analysis of Soros's theory of reflexi…
The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold's Diffusion. By adapting results and proofs from existing…
An interesting toy model has recently been proposed on Schumpeterian economic dynamics by Thurner {\it et al.} following the idea of economist Joseph Schumpeter. Punctuated equilibrium dynamics is shown to emerge from this model and some…
We present a dynamical many-body theory of money in which the value of money is a time dependent ``strategic variable'' that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus…
We consider the Cartesian product X of n finite intervals of integers and a map F from X to itself. As main result, we establish an upper bound on the number of fixed points for F which only depends on X and on the topology of the positive…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
``Self-Organised Criticality'' (SOC) is the mechanism by which complex systems spontaneously settle close to a *critical point*, at the edge between stability and chaos, and characterized by fat-tailed fluctuations and long-memory…
Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network…
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…
Data science and machine learning provide indispensable techniques for understanding phenomena at scale, but the discretionary choices made when doing this work are often not recognized. Drawing from qualitative research practices, we…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we…
Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…
A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann-Krause and Weisbuch-Deffuant). The…
This paper analyses and synthesises the Disturbance Observer (DOb) based motion control systems in the discrete-time domain. By employing Bode Integral Theorem, it is shown that continuous-time analysis methods fall-short in explaining the…