Coupled map lattices are widely used and applied in the study of dynamical systems. The iterative map of matrices was presented by the researchers of the proposed project in 2011. The replacement of a discrete scalar variable by a square matrix of order 2 in a single iterative map can yield such counterintuitive phenomena like the explosive divergence. Such behavior cannot be represented by any scalar iterative map or the lattice of coupled scalar maps. It is shown that the extended coupled map lattices of matrices of order two can generate complex fractal patterns representing spatiotemporal divergence which can be controlled by the coupling parameter between the nodes. The application of such effects of coupled map lattice of matrices varies from image hiding schemes to the investigation of biological systems.
The proposed project aims to present, investigate and apply coupled map lattices of matrices of order higher than two.
Developing the concept of coupled map lattice of matrices of order nxn opens up great scientific potential and a breakthrough can be expected in this area. The scientific experience of researchers and the publication of previous results related to coupled map lattices of matrices in high-level scientific journals show the importance and quality of the proposed research. This project aims to intensify the further investigation and application of coupled map lattice of matrices, which guarantees novel and publishable results. Implementation of project idea requires to accomplish the following four research objectives:
1. Propose a new multi-image simultaneously encoding scheme based on coupled map lattices of matrices of order nxn and develop algorithmic implementations of such a scheme.
2. Investigate and apply transient processes (such as propagating and spiral waves, solitons, chimeras) in 2-dimensional coupled map lattices of matrices and propose a control scheme for such a complex system.
3. Investigate and apply complex divergence processes (including intermittent bursting) in coupled map lattices of matrices.
4. Investigate and apply the finite-time stabilization of unstable solution to coupled map lattices of matrices. Construct and apply the Hrank-map-based stabilization scheme for unstable orbits.
It is planned to solve all four tasks during the project implementation period of 2021-2023.
It is planned to issue at least 4 publications in high-level (Q1-Q2) (and open access) scientific journals, and the results are planned to be presented at two conferences in Lithuania and two conferences abroad. The project also envisages two 15 days internships in foreign research centers.
The implementation of the proposed project together with all the planned deliverables and internships would guarantee not only a breakthrough in the investigation of nonlinear systems but would also contribute to the internationality of Lithuanian science.
Project funding:
This research project is funded by the European Social Fund according to the 2014–2020 Operational Programme for the European Union Funds’ Investments, under measure’s No. 09.3.3-LMT-K-712 activity “Promotion of postdoctoral fellowships studies”.
Project results:
The project ,,Coupled map lattices of matrices – theory and applications” (09.3.3-LMT-K-712-23-0235)” aims to intensify the breakthrough in the research and applications of coupled map lattices of iterative maps of matrices and together with publications in high-level scientific journals to contribute to increasing the internationality of Lithuanian science by preparing presentations at foreign conferences and internships at foreign research centers. On the topic of the ongoing project, two articles have already been published in the Q1 quartile and one in the Q2 quartile journals, one more scientific article has been added and intensive scientific research continues. The results were presented at two conferences (national and international).
Period of project implementation: 2021-06-15 - 2023-08-31
Project coordinator: Kaunas University of Technology
