Chaos, Multistability, and Stochastic Dynamics in Mach-Dependent Ion-Acoustic Waves
Mudassar Imran, Adil Jhangeer
Source abstract
We present a dynamical systems analysis of ion-acoustic waves in a forced plasma system, focusing on chaos, multistability, and stochastic sensitivity as functions of the Mach number. Both deterministic and stochastic versions of a reduced third-order nonlinear oscillator are studied in the subsonic, sonic, and supersonic regimes. Three-dimensional attractor reconstruction reveals a transition from periodic islands in the subsonic regime to fully developed chaos at supersonic Mach numbers. Basin geometry analysis identifies the Mach number as a structural bifurcation parameter, while Monte Carlo basin stability confirms genuine multistability. An analytical framework is developed, including fixed-point stability analysis, a center-manifold reduction with its stochastic extension, a stability map, and effective-potential analysis, all identifying a pitchfork bifurcation at the sonic threshold. Rigorous error bounds for the forced versus unforced solutions are derived. Poincaré maps, entropy measures, recurrence plots, surrogate testing, and the Kaplan–Yorke dimension confirm the increasing dynamical complexity with Mach number, and a parameter-space bifurcation analysis identifies the sonic threshold as the organizing center of the transition to chaos. Stochastic comparisons show that additive noise produces large-amplitude deviations, and the final-state distributions of the position and velocity variables are not Gaussian.
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