Multiple Attractor in Newton -Leipnik System, Peak to Peak dynamics and Chaos Control

Abstract

The chaotic properties of Newton-Leipnik system are discussed from the view point of strange attractors. Previously, two strange attractors of this system were illustrated which occured from two different initial conditions under the same parameter condition. It is found that above system also exhibits multiple attractors under different parameter values but same initial condition and we have shown the existence of three other strange attractors with varying dimensionality under different parametric conditions. The properties of these attractors are then analyzed on the basis of Lyapunov exponents, power spectra, recurrence analysis and peak-to-peak dynamics. The peak-to-peak dynamics relies on the low dimensionality of the chaotic attractor and allows to approximately model the system. Peak-to-peak plot along with return-time plot are then effectively used to solve the optimal control problem of the system which reverts the system to a periodic situation.