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arXiv · 2603.22875

Parametric Modulation of Nonlinear Coupling in the H\'enon Heiles System: Resonances, Chaos, and Stabilization

Vinesh Vijayan·P Satishkumar·Dinesh Wankhade. R Sumathi
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Abstract

We investigate parametric modulation of the nonlinear coupling in the Henon Heiles system, which directly modifies intrinsic resonance structure in a manner complementary to additive forcing. Canonical perturbation theory in extended phase space yields normal forms predicting resonance tongues scaling as $\sqrt{\varepsilon}$ near commensurate frequencies. Melnikov analysis quantifies separatrix splitting and chaos onset, confirmed by symplectic simulations showing transition from localized resonances to global transport via overlap. High-frequency averaging reveals potential stiffening that suppresses chaos. parametric modulation of nonlinear coupling provides an alternative route for generating combination resonances and influencing chaotic dynamics

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Vinesh Vijayan, P Satishkumar, Dinesh Wankhade. R Sumathi. 2026-03-24. Parametric Modulation of Nonlinear Coupling in the H\'enon Heiles System: Resonances, Chaos, and Stabilization. https://arxiv.org/abs/2603.22875

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