Time Dependent Stabilization of a Hamiltonian System

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.