energy variability approach in plasma oscillations modelled by a modified duffing equation

In many nonlinear systems, regular and chaotic behaviours are strongly linked to the energy variability of the system. energy variability plays a major role in chaotic systems. the melnikov function provides a measure of the distance between a stable and unstable manifold. if the two manifolds intersect, chaos is possible. the concept of energy variability is introduced in this work through the melnikov integral. in this paper, we apply the energy variability approach to plasma oscillations modelled by the modified duffing equation. due to the energy variability approach, the plasma oscillations show very interesting results during the evolution shown by the works. we observed periodic, quasiperiodic and chaotic oscillations in the system by adjusting the amplitude (f ) of the external excitation, energy variability parameter ( ε), quadratic (β) and cubic (δ) nonlinear parameters. control of chaos is also observed in some parameter values. the numerical results are demonstrated by a bifurcation diagram, phase plot, poincare map and time series graph.