This project aims to introduce a novel class of deterministic chaos, termed Nilpotent Chaos. The project team consists of pioneers in the theory and
application of nonlinear iterative maps involving nilpotent matrices. The central objective is to investigate whether complex phenomena—such as spiral
waves of divergence, chimera states, intermittent bursting, and finite-time divergence—previously observed in iterative nilpotent systems, can also emerge in chaotic systems governed by nonlinear differential equations that define the framework of Nilpotent Chaos. The project seeks to formulate foundational definitions of Nilpotent Chaos, support them with rigorous hypotheses and proofs, and explore their implications in real-world systems. One of the most groundbreaking aspects of this research is the extension of chaos theory to matrix-valued differential equations, where the entire system evolution—not just the initial conditions—is governed by nilpotent structures. This nodal extension represents a significant departure from traditional vector or matrix-based formulations in the mathematical theory of deterministic chaos. The project is structured around six key research objectives: 1.Development of the theoretical foundations of Nilpotent Chaos. 2.Formalization of divergence codes characteristic of Nilpotent Chaos. 3.Exploration of practical applications of divergence phenomena. 4.Extension to spatially distributed models of Nilpotent Chaos. 5.Investigation of divergence effects in spatially extended systems. 6.Analysis of solitons and solitary wave solutions within Nilpotent Chaos frameworks. By addressing a fundamental gap in the current understanding of chaotic dynamics, this project aspires to advance both theoretical and applied aspects of nonlinear science. Moreover, it aims to establish a distinct contribution of Lithuanian research to the global scientific community by pushing the boundaries of chaos theory beyond its current state-of-the-art.
Project funding:
Research Council of Lithuania, Projects carried out by researchers’ teams
Project results:
The project focuses primarily on the development of the theory of nilpotent chaos. Within the project, divergence codes for nilpotent chaos systems are formulated, studies of spatially extended models of nilpotent chaos are carried out, and soliton solutions in models of nilpotent chaos are constructed.
The results of the project will be disseminated to the scientific community. The results will be published in international peer-reviewed journals, and the project team will present their findings at relevant international conferences, encouraging discussion and collaboration within the scientific community. The project also plans to deposit research data and publications in open-access repositories in order to ensure broad accessibility.
Period of project implementation: 2025-11-03 - 2028-10-31
Project coordinator: Kaunas University of Technology
