Chaotic saddles in nonlinear modulational interactions in a plasma

TL;DR

This paper investigates chaotic dynamics in a nonlinear plasma model involving modulational interactions, identifying chaotic saddles, bifurcations, and crisis phenomena through numerical analysis of Lyapunov exponents and bifurcation diagrams.

Contribution

It introduces a detailed numerical study of chaotic saddles and bifurcations in a plasma modulational process model, revealing complex structures like shrimp-shaped regions and crisis-induced intermittency.

Findings

Identification of chaotic saddles and their manifolds.

Observation of bifurcation structures including saddle-node bifurcation.

Detection of crisis-induced intermittency linked to chaotic saddle connections.

Abstract

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.