Almost-sure asymptotic stability of a general four-dimensional system driven by real noise

DOI10.1007/BF02186871zbMath0828.60050OpenAlexW2071872064MaRDI QIDQ1897028

N. Sri Namachchivaya, Monica M. Doyle

Publication date: 18 December 1995

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02186871

zbMATH Keywords

Lyapunov exponentsrotation numbersItô equationsalmost-sure asymptotic stability

Mathematics Subject Classification ID

Stochastic stability in control theory (93E15) Stochastic analysis (60H99)

Related Items (7)

Random dynamical systems: addressing uncertainty, nonlinearity and predictability ⋮ The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise ⋮ Small noise expansion of moment lyapunov exponents for two-dimensional systems ⋮ Exponential H_∞ filtering for stochastic Markovian jump systems with time delays ⋮ Probability density and stochastic stability for the coupled Van der Pol oscillator system ⋮ Some aspects of chaotic and stochastic dynamics for structural systems. ⋮ Stabilization of linear systems by noise: Application to flow induced oscillations

Cites Work

• Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise
• A multiplicative ergodic theorem for rotation numbers
• Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
• Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small Diffusion
• Lyapunov Exponents and Stochastic Stability of Coupled Linear Systems Under Real Noise Excitation
• Sample Stability of Second Order Linear Differential Equations with Wide Band Noise Coefficients
• On the stability of two-dimensional linear stochastic systems
• Maximal Lyapunov Exponent and Rotation Number for Stochastically Perturbed Co-dimension Two Bifurcations
• A Formula Connecting Sample and Moment Stability of Linear Stochastic Systems
• Necessary and Sufficient Conditions for Almost Sure Sample Stability of Linear Ito Equations
• Diffusion Processes in One Dimension
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