Difference equations with impulses

• Autorzy: Danca Marius , Feckan Michal , Pospisil Michal

Identyfikatory

DOI

10.7494/OpMath.2019.39.1.5

• Języki publikacji: EN

Abstrakty

EN

Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.

Słowa kluczowe

EN

difference equations; impulses; stability; fixed points; Li-Yorke chaos

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 1
• Strony: 5--22
• Opis fizyczny: Bibliogr. 11 poz,

Twórcy

autor

Danca Marius

• Avram Iancu University of Cluj-Napoca Department of Mathematics and Computer Science 400380 Cluj-Napoca, Romania
• Romanian Institute of Science and Technology 400487 Cluj-Napoca, Romania

autor

Feckan Michal

• Comenius University in Bratislava Faculty of Mathematics, Physics and Informatics Department of Mathematical Analysis and Numerical Mathematics Młyńska Dolina, 842 48 Bratislava, Slovak Republic
• Slovak Academy of Sciences Mathematical Institute Stefanikova 49, 814 73 Bratislava, Slovak Republic

autor

Pospisil Michal

• Comenius University in Bratislava Faculty of Mathematics, Physics and Informatics Department of Mathematical Analysis and Numerical Mathematics Młyńska Dolina, 842 48 Bratislava, Slovak Republic
• Slovak Academy of Sciences Mathematical Institute Stefanikova 49, 814 73 Bratislava, Slovak Republic

Bibliografia

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• [2] M.-F. Danca, Chaos suppression via periodic pulses in a class of piece-wise continuous systems, Comput. Math. Appl. 64 (2012), 849-855.
• [3] M.-F. Danca, W.K.S. Tang, G. Chen, Suppressing chaos in a simplest autonomous memristor-based circuit of fractional order by periodic impulses, Chaos Solitons Fractals 84 (2016), 31-40.
• [4] S.N. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, 2005.
• [5] J. Guemez, M.A. Matias, Control of chaos in unidimensional maps, Phys. Lett. A 181 (1993), 29-32.
• [6] N.J. Higham, Functions of Matrices, Theory and Computation, SIAM, Philadelphia, 2008.
• [7] M.C. Irwin, Smooth Dynamical Systems, Academic Press, London, 1980.
• [8] M.A. Matias, J. Guemez, Stabilization of chaos by proportional pulses in system variables, Phys. Rev. Lett. 72 (1994), 1455-1458.
• [9] A.M. Samoilenko, N.A. Perestyuk, Y. Chapovsky, Impulsive Differential Equations, World Scientific, Singapore, 1995.
• [10] G. Teschl, Ordinary Differential Equations and Dynamical Systems, AMS, Providence, Rhode Island, 2010.
• [11] W.B. Zhang, Discrete Dynamical Systems, Bifurcations, and Chaos in Economics, Elsevier, Boston, 2006.