Time Dependent Stabilization of a Hamiltonian System

Asher Yahalom, Natalia Puzanov

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


In this paper we consider the unstable chaotic attractor of a Hamiltonian system with Toda lattice potential and stabilize it by an integral form control. In order to obtain stability results, we use a control function in an integral form: =u(t)=int{0}{t} k(t, s) X(s) d s SRC=JPCS17301012089ieqn1.gif in which all the back story of the process X(t) is taken into consideration. Using the exponential kernel =k(t, s)=e{-beta(t-s)} SRC=JPCS17301012089ieqn2.gif, we replace the study of integro-differential system of order 4 with an analysis of 5th order system of ordinary differential equations (without integrals). Numerical solution of the resulting system leads to the asymptotically stabilization of the unstable fixed point.

Original languageEnglish
Article number012089
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - 3 Feb 2021
Event9th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2020 - Tinos Island, Virtual, Greece
Duration: 7 Sep 202010 Sep 2020


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