L
R
Last name: LOZI
First name: René
In reflecting upon the bitcoin phenomenon, it is necessary to return to the definition of what a currency is. René Lozi recounts the history of money, and what this means for cryptocurrencies.
Complexity of a particular coordinated system is the degree of difficulty in predicting the properties of the system if the properties of the system's correlated parts are given. The coordinated system manifests properties not carried by individual parts. The subject system can be said to emerge without any "guiding hand". In systems theory and...
We introduce a novel method revealing hidden bifurcations in the multispiral Chua attractorin the case where the parameter of bifurcation c which determines the number of spiral isdiscrete. This method is based on the core idea of the genuine Leonov and Kuznetsov methodfor searching hidden attractors (i.e. applying homotopy and numerical...
We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems (generating hyperchaos; developing chaos based pseudo random number generator (CPRNG) and chaotic multistream PRNG; secure communication via...
We explore several topologies of network of 1-D coupled chaotic mapping (mainly tent map and logistic map) in order to obtain good Chaotic Pseudo Random Number Generators (CPRNG). We focus first on two-dimensional networks. Two coupled maps are studied: TTL(RC) non-alternative, and TTL(SC) alternative. In this case, those networks are...
Generation of random or pseudorandom numbers, nowadays, is a key feature of industrial mathematics. Pseudorandom or chaotic numbers are used in many areas of contemporary technology such as modern communication systems and engineering applications. More and more European or US patents using discrete mappings for this purpose are obtained by...
We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry especially in the frame of chaotic attractors for application purpose (cryptography, generic algorithms in optimization, control, ...).
Complexity of a particular coordinated system is the degree of difficulty in predicting the properties of the system if the properties of the system's correlated parts are given. The coordinated system manifests properties not carried by individual parts. The subject system can be said to emerge without any "guiding hand". In systems theory and...
Following the worldwide tradition of use of Chua's circuits for various purposes, we introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry -the design of electronic circuit- especially in the frame of chaotic attractors. An electronic circuit is composed of individual...
a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems [Aziz-Alaoui & Bertelle, 2009]. In this paper, we use the emergent property of the ultra weak multidimensional coupling of p 1-dimensional dynamical chaoticsystems which leads from chaos to randomness.Generation of...
We introduce and combine synergistically three simple new mechanisms: very weakly coupling of chaotic maps, chaotic sampling and chaotic mixing of iterated points in order to make new families of enhanced Chaotic Pseudo Random Number Generators (CPRNG). The key feature of these CPRNG is that they use chaotic numbers themselves in order to...
L'œuvre de Max Charvolen, Peintre lié à l'Ecole de Nice, est analysée dans le paradigme de la théorie de l'information.
Le travail du peintre Max Charvolen est analysé d'un point de vue mathématique. Ses mises à plats sont des projections particulières de l'espace tri-dimensionnel des objets ou des lieux du monde physique sur l'espace d'affichage bi-dimensionnel à l'aide de découpages de la toile peinte. Les deux types de bords (bords de découpe et bords de...
We propose a new mechanism for undersampling chaotic numbers obtained by the ringcoupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows thebuilding of a PRNG which passes all NIST Test.This new geometric undersampling is very effective for generating 2 parallel streams of pseudorandomnumbers, as we show, computing...
Since the famous paper of E. Lorenz in 1963 numerical computations using computers play a central role in order to display and analyze solutions of nonlinear dynamical systems. By these means new structures have been emphasized like hyperbolic and/or strange attractors. However theoretical proofs of their existence are very di¢ cult and limited...
During the last decades, it had been highlighted the duality between chaotic numbers and pseudo-random numbers. Emergence of pseudo-randomness from chaos via various under-sampling methods has been recently discovered. Instead of opposing both qualities (chaos and pseudo-randomness) of numbers, it should be more interesting to shape mixed...
Bifurcation branches of solutions of nonlinear (differential) equations dependent on a real-parameter is now a well developed theory. However, what is known is mostly bifurcate solutions in a neighbourhood of the bifurcation points, and there exist few numerical methods that allow us to obtain these branches. The method we propose allows us to...
Relationships between difference and differential equations are examined, to understand why the applications of the first to problems of real life, are not as well developed as the applications of the second. In this goal, a review of journals devoted to both types of equations is done, strengthened by the analysis of the MSC2020- Mathematics...
International audience
Recently chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Their good performances have been emphasized . In the frame of evolutionary algorithms, the use of chaotic sequences instead of random ones has been introduced by Caponetto and al. [4]. Since their...
We study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when the initial value thumbs the finite set in the increasing order. We are able to predict, using closed formulas, the number...
Recently chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Their good performances have been emphasized. In the frame of evolutionary algorithms, the use of chaotic sequences instead of random ones has been introduced by Caponetto and al. Since their original...
We propose a novel noise-resisting ciphering method resorting to a chaotic multi-stream pseudorandom number generator (denoted Cms-PRNG). This Cms-PRNG co-generates an arbitrarily large number of uncorrelated chaotic sequences. These cogenerated sequences are actually used in several steps of the ciphering process. Noisy transmission conditions...
This paper describes a new reliable numerical method for computing chaotic solutions of dynamicalsystems and, in special cases, is applied to Chen strange attractor. The numerical precision ofthe computation is finely mastered.We introduce a modification of the method of power series forthe construction of approximate solutions of the Chen...
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set X allows us to describe precisely the behaviour of such systems.We can predict bymeans of closed formulas, the number of gop of the set of all the function from X to itself. We also explore, using the brute...