In this paper the author analyzes the behavior of exchange rates expectations for four currencies, by considering a re-calculation and an extension of Resende and Zeidan (Expectations and chaotic dynamics: empirical evidence on exchange rates, Economics Letters, 2008). Considering Lyapunov...

Studies on financial markets have accumulated consistent evidences of stylized facts and anomalies, which can be characterized by stochastic switching among different co-existing market states but yet difficult to reconcile with traditionally rational expectation theory. When agents are...

The Philosophy of Blockchain Technology is concerned, among other things, with its ontology, how might it be characterised, how is it being created, implemented, and adopted, how does it operate in the world, and how does it evolve over time. Here, we concentrate on whether Bitcoin/blockchain...

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and...

In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of...

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the...

When a system becomes unstable or noise becomes excessive, often regulations of the form of limiters (barriers obstructing excursion into undesired areas of the phase space) are imposed. It is hoped that by the influence of this element, the system can be calmed and its behaviour can be...