Stochastic bifurcation for two-time-scale dynamical system with α-stable Lévy noise

DOI10.1088/1742-5468/abdeb2zbMath1504.34145OpenAlexW3135686425MaRDI QIDQ5857545

Zhigang Zeng, Shenglan Yuan, Jin-qiao Duan

Publication date: 1 April 2021

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1742-5468/abdeb2

zbMATH Keywords

stochastic processesnonlinear dynamicsstationary statessystemic stability

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Singular perturbations for ordinary differential equations (34E15) Bifurcation theory for random and stochastic dynamical systems (37H20) Bifurcation of solutions to ordinary differential equations involving randomness (34F10)

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Cites Work

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• Bifurcation of the Hodgkin and Huxley equations: A new twist
• A stochastic version of center manifold theory
• Transverse bifurcations of homoclinic cycles
• Elementary bifurcations for a simple dynamical system under non-Gaussian Lévy noises
• Hopf bifurcation from fronts in the Cahn-Hilliard equation
• Continuation and Bifurcation of Grain Boundaries in the Swift--Hohenberg Equation
• Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions
• VOLATILITY EFFECTS ON THE ESCAPE TIME IN FINANCIAL MARKET MODELS
• Nonlinear PDEs
• A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise
• The random walk's guide to anomalous diffusion: A fractional dynamics approach