René Lozi of Université Côte d’azur

Abstract: We introduce the paradigm of mathematical circuits, which share similarities with that of electric circuitry, to combine chaotic attractors and their networks for real-world applications. Invented about fifty years ago, chaotic attractors are no longer a mere curiosity but are used in multiple real and industrial applications (cryptography-based chaos, secure communications via synchronization, chaos-based hash functions, pseudo-random number generator (CPRNG), generic algorithms, control, memristors, chimeras, etc.).

Research on these attractors is flourishing, whether to find more efficient ones or to combine them into extended networks using multiple topologies. However, the classical mathematical formulas that define them do not provide a direct insight into their structure and the topology of their network when hundred of attractors are combined to produce chimeras and solitary states.

Inspired by the paradigm of electric circuitry, based on specialized devices, we introduce basic mathematical elements like generator, coupler, reducer, undersampler, cascader, etc., representing the components of chaotic attractors and their different possible coupling. Each of them is defined by the combination of mathematical formulas. We give some rules for assembling them into circuits. This theory of mathematical circuits facilitates the search for new multidimensional chaotic attractors and the study of new topologies of groups of chaotic attractors of different types.

Biography:

René LOZI is Emeritus Professor at University Côte d’Azur, Dieudonné Center of Mathematics, France. He completed a PhD in 1975 and the French State Thesis (on chaotic dynamical systems) under the supervision of Prof. René Thom (Fields medalist) in 1983.

In 1991, he became Full Professor at University of Nice and IUFM (Institute for teacher trainees). He has served as Director of this institute (2001-2006) and as Vice-Chairman of the French Board of Directors of IUFM (2004- 2006). He is a member of several editorial boards of international journals. In 1977, he discovered a particular mapping of the plane having a strange attractor (now, commonly known as "Lozi map").

Nowadays, his research areas include complexity and emergence theory, dynamical systems, bifurcations, control of chaos, cryptography based on chaos, memristors (physical devices for neurocomputing) and artificial intelligence. He is working in those fields with renowned researchers from many countries. He received the Dr. Zakir Husain Award 2012 from the Indian Society of Industrial and Applied Mathematics during the 12th biannual conference of ISIAM at the University of Punjab, Patialia, (India) in January 2015. He received the C.S. Hsu Award 2024 for distinguished scholars in Nonlinear Dynamics and Control, issued annually by the Nonlinear Science and Complexity Conferences Series, in August 2024 at the Sichan university of Yibin, China, and the Complex Systems and Nonlinear Dynamics Award, during the 12th International Conference on Image processing, Wavelet and Application, in November 2025 at Istanbul Technic Uuniversity.

In 2023-25, he was Vice-President of the International Society of Difference Equations.

Address:University Côte d’Azur, Dieudonné Center of Mathematics, , Nice, Provence-Alpes-Cote d'Azur, France