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On The Properties of a Chaotic Attractor Observed in an Inhomogenous Magnetised Plasma

The equations governing the non-linear dynamics of low frequency, long wave-length electromagnetic fields in a non-uniform magnetised plasma are discussed. This pair of non-linear partial differential equations turns out to be non-integrable. A Galerkin basis type expansion is then used to deduce six coupled non-linear ordinary differential equations. These equations are then analysed from the viewpoint of stability and chaos. The system is treated numerically using the techniques of Power spectrum. Lyapunov exponent and phase space analysis. The various regions of the attractor are quantified using the concept of local divergence rate and the corresponding time averages. The predictability property of the various sections is also analysed by studying the probability density functions of such time averages. Furthermore, the phase spatial variation of the predictability is studied using the Poincaré section for different sections of incoming and outgoing orbits separately. The local divergence rate of these different sections are also computed to detail the behaviour of the attractor. The chaotic scenario of the attractor is controlled using (a) adaptive control method (b) application of a short pulse (c) application of a nonlinear pulse on the Poincaré section.