René Pierre Lozi

Université Côte d'Azur · Mathematics

(to appear in September Issue) Memristor, the missing fourth passive circuit element predicted forty years ago by L. O. Chua was recognized as a nanoscale device in 2008 by researchers of a H.P. Laboratory. Recently the notion of memristive systems was extended to capacitive and inductive elements, namely, memcapacitor and meminductor whose propert...

This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: TTL rc non-alternate, and TTL SC alternate. The primary idea of the novel maps has been based on an...

The increasing number of e-transactions requires more secure and innovative schemes for secure information storage and transmission. Since the encryption should be unique for each transaction, there is a big necessity of new generators of very huge numbers of encryption keys, and chaotic random number generators seem to be perfectly suitable for th...

We introduce a novel method revealing hidden bifurcations in the multispiral Chua attractor in the case where the parameter of bifurcation c which determines the number of spiral is discrete. This method is based on the core idea of the genuine Leonov and Kuznetsov method for searching hidden attractors (i.e. applying homotopy and numerical continu...

Letter in response to the article of Jean-Paul Delahaye “Cryptocurrencies and Blockchains” in the same revue (Vol. 2, No. 4). This paper discuss soe points concerning the sustainability of bitcoins and cryptocurrencies. There is a response of Jean-Paul Delahaye to this letter.

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is pleased to present Volume 2, Issue 2, featuring a carefully curated collection of eight research articles that contribute to the development of applied mathematics and scientific computing. This issue reflects the journal’s steadfast dedication to fostering schola...

https://dergipark.org.tr/en/pub/chaos/issue/88057

Over the past fifty years, the development of chaotic dynamical systems theory and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. Chaotic attractors are not a fleeting curiosity, and their continued study is important for the progress of mathematics. This book collects...

The main purpose of this paper is to analyze the stability of fixed points in a new fractional discrete system induced by a continuous differential system of fractional order and to explore its bifurcations. From the fractional order differential Arneodo’s system, we derive a new discrete chaotic dynamical system. Asymptotic stability of the first...

https://dergipark.org.tr/en/pub/chaos/issue/86422

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is a peer-reviewed, open-access international journal, published semiannually by the University Center Abdelhafid Boussouf in Mila, Algeria. JIAMCS is dedicated to disseminating high-quality original research and comprehensive review articles across various fields, in...

https://dergipark.org.tr/en/pub/chaos/issue/83761

This book presents contributions related to new research results presented at the 27th International Conference on Difference Equations and Applications, ICDEA 2022, that was held at CentraleSupélec, Université Paris-Saclay, France, under the auspices of the International Society of Difference Equations (ISDE), July 18–22, 2022. The book aims not o...

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional $ \mathcal {R}_0 $ which is based on the disease-free equilibrium, and a new net...

This article is devoted to the first steps of nine mathematicians from five countries on their path to mathematics, chaos and discrete dynamical systems, some from early childhood. In these life stories, the names of outstanding mathematicians arise, crisscrossing the nine stories in unexpected ways. These mathematicians also interacted with each o...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open-access, peer-reviewed semiannual international journal published by the Abdelhafid Boussouf University Center of Mila, Algeria. The journal publishes high-quality original research and review papers from various fields related to applied mathematics,...

UDC 517.9 Despite having low rates of tuberculosis (TB) mortality in many countries, like China, Europe, and the United States, other countries, like India continue to struggle to contain the epidemic. This study intends to examine the effects of vaccinations and treatments on the dynamics of TB in two countries, Ukraine and Algeria, with contraste...

https://dergipark.org.tr/en/pub/chaos/issue/80150

The Department of Mathematics, University Center Abdelhafid Boussouf of Mila, Algeria, in collaboration with the Laboratory of Mathematics and their Interactions, organizes the International Conference on Contemporary Mathematics and its Applications (ICCMA 2023). This conference will adopt both online and face-to-face participation. It aims to bri...

This foreword presents the 32 articles of the special issue devoted to the Lozi, Hénon and other chaotic attractors proposed by 78 authors from 20 countries (Algeria, Brazil, Canada, China, Czech Republic, France, Germany, India, Italy, Jamaica, Japan, Lebanon, New Zealand, Portugal, Russia, Saudi Arabia, Spain, Ukraine, Tunisia, USA). These origin...

Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure and applied its properties in many fields (e.g., improvement of physical devices, electrical components such as memristors, cryptography, optimization, evolutionary algorithms,...

The global information technology (IT) industry accounts for approximately 2% of the world's greenhouse gas emissions, equivalent to the aviation industry's emissions. Moreover, IT energy consumption is projected to increase by 5% annually, and the industry is expected to consume 21% of the world's electricity by 2030. Therefore, there is a growing...

https://dergipark.org.tr/en/pub/chaos/issue/77246

Despite low tuberculosis (TB) mortality rates in China, Europe, and the United States, many countries are still struggling to control the epidemic, including India, South Africa, and Algeria. This study aims to contribute to the body of knowledge on this topic and provide a valuable tool and evidence-based guidance for the Algerian healthcare manag...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by the University Center Abdelhafid Boussouf, Mila, Algeria. The journal publishes high-quality original research and review papers from various fields related to applied mathematics, s...

Since its original publication in 1978, Lozi's chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure or applied its properties in many fields (electronic devices such as memristors, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming th...

This article discusses the multispiral Chua Chaotic attractor's hidden bifurcations that are generated by the sine function. The number of spirals (also known as a multiscroll attractor) that are controlled by the integer parameter c can be used to describe the basic shape of chaotic attractors. Since this parameter is an integer, increasing it by...

Since its original publication 1 in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications analyze its particular structure or apply its properties in many fields (electronic devices like memristor, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial...

This paper investigates the right Hadamard fractional differences. First, a Q-operator is defined for continuous Hadamard fractional calculus. It shows that the left and right Hadamard operators satisfy a dual identity. Then, the Q-operator is extended to define the right Hadamard fractional sum and difference, and present their properties. Initial...

Call for papers: The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) calls scholars, academics, scientists, and researchers worldwide to submit their original papers for inclusion in our upcoming issue (Volume: 03, Issue: 01, January to June 2023). JIAMCS welcomes high-quality original research papers in all areas of...

https://dergipark.org.tr/en/pub/chaos/issue/75756

In this paper, a modified hyperchaotic memristor-based Chua's circuit and its generalized discrete model are reported. First, the dynamics of the continuous system are investigated using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams, showing that the proposed circuit model possesses a lin...

Memristors close the loop for I-V characteristics of the traditional, passive, semi-conductor devices. A memristor is a physical realisation of the material implication and thus is a universal logical element. Memristors are getting particular interest in the field of bioelectronics. Electrical properties of living substrates are not binary and the...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by the Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila, Algeria. The journal publishes high-quality original research and review papers from various fi...

This paper investigates the modified projective synchronization (MPS) between two hyperchaotic memristor-based Chua circuits modeled by two nonlinear integer-order and fractional-order systems. First, a hyperchaotic memristor-based Chua circuit is suggested, and its dynamics are explored using different tools, including stability theory, phase port...

This Issue is dedicated to some selected papers of the International Conference on Mathematics and Applications (ICMA'2021), held on December 7-8, 2021, at Blida 1 University, Algeria. Guest Editor: Mohammed Hachama Associet Editors: - Benbachir Maamar -Redouane Boudjemaa ARK: https://n2t.net/ark:/49935/jiamcs.v2i2 Published: 10-09-2022

This work proposes a new secure chaos-based encryption/decryption system, operating in cipher block chaining (CBC) mode, and analyze its performance. The cryptosystem includes a robust pseudorandom number generator of chaotic sequences (PRNG-CS). A strong chaos-based S-box is proposed to perform a circular substitution operation (confusion process)...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by the Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila, Algeria. The journal publishes high-quality original research and review papers from various fi...

Nowadays chaos-based cryptography systems are widely used to protect sensitive data. A variety of chaos-based cryptosystems with software implementation has been published in the literature. However, due to the rapid growth of connected devices, the development of hardware secure and low-resource cryptographic systems is necessary. In this paper, w...

Nowadays, mankind is living in a cyber world. Modern technologies involve fast communication links between potentially billions of devices through complex networks (satellite, mobile phone, Internet, Internet of Things (IoT), etc.). The main concern posed by these entangled complex networks is their protection against passive and active attacks tha...

The fractional-order derivative of a non-constant periodic function is not periodic with the same period. Consequently, any time-invariant fractional-order systems do not have a non-constant periodic solution. This property limits the applicability of fractional derivatives and makes it unfavorable to model periodic real phenomena. This article int...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by the Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila, Algeria. The journal publishes high-quality original research and review papers from various fi...

In this paper, a novel epidemiological model describing the evolution of tuberculosis in a human population is proposed. This model is of the form SEIR, where S stands for Susceptible people, E for Exposed (infected but not yet infectious) people, I for Infectious people, and R for Recovered people. The main characteristic of this model inspired fr...

Memristors close the loop for I-V characteristics of the traditional, passive, semi-conductor devices. A memristor is a physical realisation of the material implication and thus is a universal logical element. Memristors are getting particular interest in the field of bioelectronics. Electrical properties of living substrates are not binary and the...

Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to “reconstruct” some supposed influences. In the 1970s, a new way of performing science under the name “chaos” emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a...

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed S...

Nowadays, mankind is living in a cyber world. Modern technologies involve fast communication links between potentially billions of devices through complex networks (satellite, mobile phone, Internet, Internet of Things (IoT), etc.). Moreover, these devices can be affected by various categories of security. This imposes to design new cryptographic m...

Based on the Hodgkin–Huxley and Hindmarsh–Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the...

This article highlights particular mixed-mode oscillations (MMO) based on canard explosion observed in a fractional-order Fitzhugh-Nagumo (FFHN) model. In order to rigorously analyze the dynamics of the FFHN model, a recently introduced mathematical notion, the Hopf-like bifurcation (HLB), which provides a precise definition for the change between...

Memristors close the loop for I-V characteristics of the traditional, passive, semiconductor devices. Originally proposed in 1971,the hunt for the memristor has been going ever since. The key feature of a memristor is that its current resitance is a function of its previous resistance. As such, the behaviour of the device is influenced by changing...

This article introduces a new model of weighted human behaviour in the context of urban terrorist attacks. In this context, one of the major challenges is to improve the protection of the population. In achieving this goal, it is important to better understand and anticipate both individual and collective human behaviour, and the dynamics of the di...

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and...

In this paper, hidden bifurcation routes to multiscroll chaotic attractors generated by saturated function series are explored. The method to nd such hidden bifurcation routes (HBR) depending upon two parameters is similar to the method introduced by Menacer, et al. (2016) for Chua multiscroll attractors. These HBR are characterized by the maximal...

In this work we investigate the emergence of mixed-mode oscillations and canard explosion, in a planar fractional-order FitzHugh-Nagumo model (FFHN). An algorithm, called Global-Local Canard Explosion Search Algorithm (GLCESA) is developed and used to investigate the existence of canard oscillations in the neighbourhoods of Hopf-like bifurcation po...

This article investigates the complex phenomena of canard explosion with mixed-mode oscillations, observed from a fractional-order FitzHugh–Nagumo (FFHN) model. To rigorously analyze the dynamics of the FFHN model, a new mathematical notion, referred to as Hopf-like bifurcation (HLB), is introduced. HLB provides a precise definition for the change...

In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurcation graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of the...

In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurca- tion graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of t...

The purpose of this article is to introduce a novel method for unveiling hidden patterns of even number of spirals in the multi-spiral Chua Chaotic attractor. This method is based on the duration of integration of this system and allows displaying every pattern containing from 1 to c+1 spirals of this attractor. After having given the equation of t...

In this paper, we design and implement two new stream ciphers based on Pseudo Chaotic Number Generators (PCNGs) which integrate discrete chaotic maps, namely, Piecewise Linear Chaotic Map (PWLCM), Skewtent and Logistic map. They are weakly coupled by a predefined matrix A for the first PCNG and they are coupled by a binary diffusion matrix D for th...

The study of nonlinear dynamics is relatively recent with respect to the long historical development of early mathematics since the Egyptian and the Greek civilization, even if one includes in this field of research the pioneer works of Gaston Julia and Pierre Fatou related to one-dimensional maps with a complex variable, nearly a century ago. In F...

Cinq approches différentes pour une même œuvre plastique sont réunies dans le cahier de la revue Il Particolare numéro 29/30. Cinq spécialistes de champs disciplinaires différents interrogent une œuvre résolument artistique se revendiquant comme picturale – et exclusivement picturale. Jacques Beauffet, historien de l’art, Diana Gay, conservatrice,...

This article is devoted to the study of several topologies of complex networks of chaotic maps, in order to design new Chaotic Pseudo Random Number Generators for cryptographic purpose in a bottom up approach of doing mathematics. We examine topologies of special 2 -D coupled maps which are built combining piecewise linear and logistic maps. We pre...

The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business t...