In this article, we specify the different approaches followed by the economists and the financial economists in order to use chaos theory. We explain the main difference using this theory with other research domains like the mathematics and the physics. Finally, we present tools necessary for...

We study the one-dimensional logistic map with parametric perturbation. Using a small periodic function as the perturbation, new attractors may appear. Beside these new attractors, complex attractors exist and are responsible for transients in many trajectories. We observe that each one of these...

Waiting time indicators are defined by measuring the time needed for a point x to approach a given point y. Our aim is to test the use of waiting time indicators, and quantitative recurrence ones to numerically estimate the local dimension of attractors in dynamical systems, as suggested by some...

Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.

The crisis begins when one or several variables of the economic system tend to move towards the borders of the "safety beach"; their behavior becomes unstable and abnormal, in other words, it becomes chaotic. The intensity of the installation of this abnormality increases and at some point...

Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.

The preponderance of the linear approach in the stock market modeling is the result of the Frisch-Slutsky paradigm which implies that the market can only converge to an equilibrium point or diverge, according to a monotonic or oscillatory trajectory. Moreover, this description of reality is...