Bifurcations in Asymptotically Autonomous Hamiltonian Systems Subject to Multiplicative Noise

DOI10.1142/S0218127422501644zbMath1506.34075arXiv2112.00548MaRDI QIDQ5040469

O. A. Sultanov

Publication date: 14 October 2022

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.00548

zbMATH Keywords

stabilityLyapunov functionbifurcationaveragingstochastic perturbationasymptotically autonomous system

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Averaging method for ordinary differential equations (34C29) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcation of solutions to ordinary differential equations involving randomness (34F10)

Related Items (1)

Long-Term Behaviour of Asymptotically Autonomous Hamiltonian Systems with Multiplicative Noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The transition from ergodic to explosive behavior in a family of stochastic differential equations
• Synchronization in a nonisochronous nonautonomous system
• On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation
• Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
• Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping
• Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances
• Stability by Liapunov's direct method. With applications
• Bifurcations of asymptotically autonomous differential equations
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The separation of motions in systems with rapidly rotating phase
• Additive noise destroys a pitchfork bifurcation
• Asymptotically autonomous differential equations in the plane
• The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise
• Analysis I. Integral presentations asymptotic methods
• Averaging for Hamiltonian systems with one fast phase and small amplitudes
• Lyapunov exponents for small random perturbations of Hamiltonian systems.
• Asymptotic expansions with exponential, power, and logarithmic functions for non-autonomous nonlinear differential equations
• Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
• Autoresonance in oscillating systems with combined excitation and weak dissipation
• Capture into parametric autoresonance in the presence of noise
• Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation
• Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Stochastic stability and control
• TOWARD AN UNDERSTANDING OF STOCHASTIC HOPF BIFURCATION
• Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model
• ESCAPING DYNAMICS IN THE PRESENCE OF DISSIPATION AND NOISE IN SCATTERING SYSTEMS
• Stability of a Stochastic Two-Dimensional Non-Hamiltonian System
• Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
• Stability, instability, and bifurcation phenomena in non-autonomous differential equations
• Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III
• Stability and Bifurcation of a Class of Stochastic Closed Orbit Equations
• STABLE AND OSCILLATING MOTIONS IN NONAUTONOMOUS DYNAMICAL SYSTEMS. A GENERALIZATION OF C. L. SIEGEL'S THEOREM TO THE NONAUTONOMOUS CASE
• Stability, Instability and Chaos
• Hopf bifurcation with additive noise
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation
• NOISE-INDUCED PATTERN FORMATION AND SYNCHRONIZATION IN A SQUARE-LATTICE NEURONAL NETWORK
• Bifurcation in Mean Phase Portraits for Stochastic Dynamical Systems with Multiplicative Gaussian Noise
• Stabilization and Destabilization of Nonlinear Differential Equations by Noise
• Damped Perturbations of Systems with Center-Saddle Bifurcation
• On asymptotic stability and instability with respect to a fading stochastic perturbation
• BIFURCATIONS AND CONTINUOUS TRANSITIONS OF ATTRACTORS IN AUTONOMOUS AND NONAUTONOMOUS SYSTEMS
• The behavior of a conservative system under the action of slight friction and slight random noise
• Stability and bifurcation phenomena in asymptotically Hamiltonian systems
• Stochastic bifurcation
• Stochastic differential equations. An introduction with applications.

This page was built for publication: Bifurcations in Asymptotically Autonomous Hamiltonian Systems Subject to Multiplicative Noise