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Safieddine Bouali

Assistant Professor in Economics, 

University of Tunis, 

Management Institute,

41, rue de la Liberté,  2000 le Bardo,

Tunisia

 

 

 

 

 

 

 


 

Education:

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, 2019-2020

Microeconomics

 

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:

-Chaos Theory:

 

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 finite phase spaces.

1/ Strange Attractor Type I :

Monarch Safye.jpg

 

 

 

 

 

 

 

 

The paper published in the International Journal of Bifurcation and Chaos (1999), 9, 4, 745-756:

cover-ijbc.gif

 

 

 

 

 

 

The PDF version available here: Bouali Safi-Chaos 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:
 

Images des mathematiques

 

It includes for example such two elegant figures :

2019 images des mathematiques

Fig.1. Starting from two different initial conditions, simulations of the dynamical system converge to the same attractor.

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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 :

Type

 

 

 

 

 

 

 

The research paper was published in Nonlinear Dynamics (2012), 70, pp. 2375–2381.

DOI 10.1007/s11071-012-0625-6

nodyn.jpg

 

 

 

 

 

 

 

The PDF version available here:nody2.pdf nody2.pdf 

Simulation and Animation by the Mathematical Imagery pathfinder Jos Leys :

 

3/ Strange Attractor Type III :

Type

 

 

 

 

 

 

 

 

The paper :

A 3D Strange Attractor with a Distinctive Silhouette. The Butterfly Effect Revisited 

 

A Mathematical Imagery and Simulation Designed by the Maths & Arts creator Jos Leys :

 

4/ Strange Attractor Type IV : 

Attractor bouali iv

The paper :

Basins of Attraction Plasticity of a Strange Attractor with a Swirling Scroll

 

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 :

 

The e-print:

A Versatile Six-wing 3D Strange Attractor

 

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:

Strange Attractor Morphogenesis by Sensitive Dependence on Initial Conditions

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:

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:

 

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(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:

 

 Bax(a)Lac 107(b)

Lac 109(c) Lac 1088(d)

       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

The paper:

A New Hyperchaotic Attractor with Complex Patterns 

 

An artistic animation by the maths & Arts pathfinder Jos Leys  :

 

2/ Hyperchaotic 4D Strange Attractor B:

 

(a)Bouali attractor 44 (b)Bouali attractor 46

(c)Bouali attractor 42(d)Bouali attractor 41

            3D projections of the phase portrait of the Attractor

                      (a), (b), (c), and (d) are the different representations

                                            of the Hyperchaotic Attractor

 

 The paper :

A Novel 4D Hyperchaotic Attractor with Typical Wings

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:

Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, Vol. 6, pp. 48-58.

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Cover images, figures and graphics of the paper are kindly provided by Jos Leys.

 

 

 


 


-Complex Systems:

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:

 

Cyclone

Idealized Tropical Cyclone; Aerological circulation follows a quasi-torus structure

(front slice removed to display its internal structure).

Coauthored paper by: 

Safieddine Bouali and Jos Leys (2013): "Tropical Cyclone Genesis: A Dynamician’s Point of View", pp. 187-192, in:

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.

 Complexity

link:

http://www.springer.com/physics/complexity/book/978-3-642-33913-4


 

-Network Economics

We study in this paper 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", Journal of Telecommunications Policy, Elsevier (available online 17/07/2017).

Jtpo

Abstract:

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.

 

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