Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise

Abstract

Stationary states for a particle moving in a single-well, steeper than parabolic, potential driven by Lévy noise can be bi-modal. Here, we explore in details conditions that are required in order to induce multimodal stationary states having more than two modal values. Phenomenological arguments determining necessary conditions for emergence of stationary states of higher multimodality are provided. Basing on these arguments, appropriate symmetric single-well potentials are constructed. Finally, using numerical methods it is verified that stationary states have anticipated multimodality.

15 pages 10 figures

References in corpus (5)

• Lévy walks
• Escape driven by $\alpha$-stable white noises
• Stationary states in Langevin dynamics under asymmetric Lévy noises
• Transport in a Levy ratchet: Group velocity and distribution spread
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Cited by in corpus (7)

• Lévy noise-driven escape from arctan potential wells
• Multimodal stationary states under Cauchy noise
• Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
• Nonlinear friction in underdamped anharmonic stochastic oscillators
• Resetting induced multimodality
• Role of long jumps in Lévy noise induced multimodality
• How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme