Assistant Professor in Economics
University of Tunis,
41, rue de la Liberté,
2000 le Bardo, Tunisia
PhD. in Theoretical Economics, University of Rennes 1, France, February 2001.
Master Degree in Economics, University of Tunis, Tunisia, December 1989.
Courses presently taught:
*First Semester, 2015-2016
-Safety and Risk Control
*Second Semester, 2015-2016
-Globalization and International Economics
Current Research Interests:
Historically, Edward Norton Lorenz established in 1963 the first strange attractor ever discovered. These amazing mathematical objects report chaotic dynamical patterns from deterministic equations. The related oscillations in a finite portion of time aren’t predictable and never resume a same path.
Strange attractors are they three-dimensional objects? Rather mathematical behaviors ! These are the displays of deterministic dynamics and cannot be summarized by a given frequency.
Explicitly oriented to the simplest exhibition of these dynamics, with very teensy mathematical tools, the purpose of this web-page aims to oversimplify to the young students the Chaos Theory.
In this e-page, we present our own research which led to new classes of 3D & 4D Strange Attractors.
See menu for further technical details and also beautiful pictures created by the Mathematics & Art pathfinder : Jos Leys.
I. 3D Strange Attractors
The chaotic dynamics are non-standard flots, but can be represented in a finite phase spaces.
1/ Strange Attractor Type I :
The paper published in the International Journal of Bifurcation and Chaos (1999), 9, 4, 745-756:
The PDF version available here: Bouali Safi-Chaos
Simulation and Animation by the wizard of Mathematical Imagery Jos Leys :
2/ Strange Attractor Type II :
The research paper was published in Nonlinear Dynamics (2012), 70, pp. 2375–2381.
The PDF version available here: nody2.pdf
Simulation and Animation by the Mathematical Imagery pathfinder Jos Leys :
3/ Strange Attractor Type III :
The paper :
Mathematical Imagery and Simulation Designed by the Maths & Arts creator Jos Leys :
4/ Strange Attractor Type IV :
The paper :
Beautiful simulations made by Jos Leys :
II. Hyperchaotic Attractors
The Science of Process mixing order and disorder can be extended to the space of dimension four. Here too there are strange attractors !
1/ Hyperchaotic 4D Strange Attractor A:
3D projections of the 4D Hyperchaotic Attractor
(a), (b), (c), and (d) are part views of the Attractor since the overall
representation of the 4D space is unrealizable
An artistic animation by the maths & Arts pathfinder Jos Leys :
2/ Hyperchaotic 4D Strange Attractor B:
3D projections of the phase portrait of the Attractor
(a), (b), (c), and (d) are the different representations
of the Hyperchaotic Attractor
The paper :
Awesome simulation and Animation by Jos Leys :
The article "Hidden Structure and Complex Dynamics of Hyperchaotic Attractors",
analyzing the two hyperchaotic systems is published in:
Cover images, figures and graphics of the paper are kindly provided by Jos Leys.
In a wide range of nonlinear phenomena, dynamical behavior can be suitably formulated with differential equations.
We explored also theoretical fields far from our Economics Education.
Tropical Cyclone Dynamics:
Idealized Tropical Cyclone; Aerological circulation follows a quasi-torus structure
(front slice removed to display its internal structure).
Coauthored paper by:
Proceedings of the 4th International Interdisciplinary Chaos Symposium
Stavrinides, S.G., Banerjee, S., Caglar, S.H., Ozer, M. (Eds.)
2013, XV, 581 p. 236 illus.