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Many conventional experimental analyses have helped us to understand most of the properties of plasma wave interactions and its behavior; nonlinear dynamics has helped us to enhance our analysis. In this paper we have tried to analyze a plasma jerk system for an ion cyclotron plasma oscillation in a magnetic field by including a higher-order source term caused by large-amplitude fluctuations. The multistability and antimonotonicity properties of the plasma system are discussed which were not explored earlier. We have also shown that the large-amplitude limit cycle in the original jerk system model of plasma is now reduced to a much smaller chaotic cycle for the new proposed system with higher-order source term.

Dynamical properties of a two-dimensional airfoil model with higher-order strong nonlinearities are investigated. Firstly, a state-space model is derived considering the plunge and pitch stiffnesses as generalized functions. Then, a stiffness function having square, cubic, and fifth-power nonlinearities is considered for both plunging and pitching stiffnesses, and the dimensionless state equations are derived. Various dynamical properties of the proposed model are investigated using equilibrium points, eigenvalues, and Lyapunov exponents. To further analyze the dynamical behavior of the system, bifurcation plots are derived. It is interesting to note that the new airfoil model with higher-order nonlinearities shows multistability with changing airspeed, and there are infinitely countable number of coexisting attractors generally called as megastability. Both multistability and megastability features of the airfoil model were not captured earlier in the literatures. To be clear, it is the first time a megastable feature is exposed in a physical system. Finally, to analyze the multifrequency effects of the airfoil model, we have presented the bicoherence plots.