ORCID iD: 0000-0002-4901-0221
Assistant Professor in Economics,
University of Tunis,
41, rue de la Liberté, 2000 le Bardo,
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, 2020-2021
Courses taught the academic year 2018-2019:
*Industrial Risk Management and Theories of Accident (causation and prevention)
*Economic Outlook Analysis
*Digital Economy and Value Creation
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.
We present also our own research on the Tunisian Telecommunication Market.
- Economics under the Covid-19 Threat:
The current pandemic could expand oppotunistic ploys between firms ! We present below a paper on the ability of the contractual theory to prevent such exploitative practices.
I. 3D Strange Attractors
The chaotic dynamics are non-standard flots, but can be represented in 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
Such "Sculptures of Chaos" are presented and simulated in an e-paper co-authored with Jos Leys at the site "Images des Mathématiques", affiliated to the CNRS, France:
It includes for example such two elegant figures :
Fig.1. Starting from two different initial conditions, simulations of the dynamical system converge to the same attractor.
Fig.2. For a particular parameters, the system leads to two attractors in separate basins from close initial conditions..
Here, a YouTube 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 :
A Mathematical Imagery and Simulation Designed by the Maths & Arts creator Jos Leys :
4/ Strange Attractor Type IV :
The paper :
A beautiful simulation of the Attractor 4 "solo" made by Jos Leys :
Simultaneous simulations of the two attractors in their respective basins by Jos Leys :
5/ Strange Attractor Type V :
A new intentionally constructed model exhibiting double, four- or even six-wing strange attractor is investigated. We point out that under the influence of the scalar parameters, such versatile chaotic attractors are obtained.
The model presentation with simulations of the double-, four- and six-wing attractor in the following ( beautiful !) film made by Jos Leys:
II. 4D Chaotic Attractors
The e-print HAL, archives.ouvertes.fr:
It is acknowledged that a strange attractor is locally unstable but globally stable. Our experiementation displays that strange attractors could be unstable at all scales. Coexistence of distinct strange attractors found not by the modification of an unique or several parameters but surprisingly by slight initial condition changes.
The 4D system:
x, y, z, and v, state variables.
It is expected that such system converges asymptotically to an unique strange attractor for any initial conditions. However, the following portraits projected to the (x, y, z) phase space are related to small changes of these conditions:
(a) A typical morphology obtained for ICa=( xa, ya, za, va)= (2, 2, 2, 2), (b) Another distinct morphology obtained for ICb=( xb, yb, zb, vb)= (0.5, 0.5, 0.5, 0.5), (c) A more complex morphology obtained for ICc=( xc, yc, zc, vc)= (0.05, 0.05, 0.05, 0.05), and (d) A Lemon-like shape for ICd=( xd, yd, zd, vd)= (1, 1, 1, 1).
Figure 1. Morphological Plasticity of the Phase Portraits
Such sensitive dependence on initial conditions is illustrated in this simulation, Bouali attractor 4D - Morphogenesis, by Jos Leys:
III. 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.
We studied the competition of the mobile network operators in the Tunisian market of telecommunications:
"Regulated termination rates and competition among Tunisian mobile network operators. Barriers, bias, and incentives",
Telecommunications Policy, 41 (2017), 573–586.
To Download :Sbouali tpy (1.36 Mo)
Since 2006, the Tunisian National Regulatory Authority has been imposing multiannual mobile-to-mobile termination rates, first on the duopoly of Tunisie Télécom and Tunisiana, and then on all three providers once Orange Tunisie entered the market in 2010.
This research studies the interplay between interconnection rates for mobile call termination and the retail price competition for prepaid SIM cards, predominantly chosen by Tunisian consumers. We show that the duopoly was practicing “price alignment” for off-net calls, and that subsequently, the third provider entering the market sparked a decisive initial price drop associated with the non-reciprocal rate it enjoyed.
However, the price war, which benefited consumers, only occurred when the Regulatory Body eliminated differential tariffs between on and off-net calls in the retail market. It follows that, everything else being equal, an interconnection rate drop alone will not lead to a decrease in retail prices.
A Research Paper on the Opportunistic Behavior between Firms and Unleashed by the Covid-19 Pandemic:
in the Journal of Research in Business and Management, Volume 8 ~ Issue 7 (2020) pp: 01-10.
The visit counter was previously reset when it exceeded 8,000.