Seminário de Sistemas Dinâmicos

Resumo:

We developed the theory to get interval eigenvalues via Constraint Interval Arithmetic (CIA). The theory is applied to the classification of the hyperbolic singularities to 2-bidimensional and 3-dimensional interval linear differential equations . We also present the ideas to calculate the interval eigenvalues using the standard interval arithmetic.

Authors: Marina T. Mizukoshi, Alain Jacquemard(Université Bourgogne Franche-Comté) and Weldon A. Lodwick.

Bibliography
1) Mizukoshi, M. T., Lodwick, W. A.: The Interval Eigenvalue Problem Using Constraint Interval Analysis with an Application to Linear Differential Equations: A First Step Toward the Fuzzy Eigenvalue Problem. Fuzzy Sets and Systems (2019), submitted.
2)Hladík, M.: Bounds on eigenvalues of real and complex interval matrices.
Appl. Math. Comput. \textbf{10}(219), 5584--5591 (2013).
3) Bonnard, B., Faugére, J.C., Jacquemard A., Safey El Din, M., Verron, T. : {Determinantal Sets, Singularities and Application to Optimal Control in Medical Imagery}, Proc. {ISSAC},{103--110}, {2016}.
4) LODWICK, W., Interval and Fuzzy Analysis: A
Unified Approach In: Advances in Imaging and Electron Physics, Volume 148, Edited by Peter W. Hawkes Academic Press, 2007.
5)Mizukoshi, Marina Tuyako; Jacquemard, Alain ; Lodwick, Weldon Alexander . Classification of Hyperbolic Singularities in Interval 3-Dimensional Linear Differential Systems. Communications in Computer and Information Science. 1ed.New York: Springer International Publishing, 2020, v. 1238, p. 13-27.