The effects of small noise on implicitly defined nonlinear dynamical systems

DOI10.1109/TCS.1983.1085404zbMath0527.93063OpenAlexW2132535069MaRDI QIDQ3309729

Shankar S. Sastry

Publication date: 1983

Published in: IEEE Transactions on Circuits and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tcs.1983.1085404

zbMATH Keywords

small random perturbationsstochastic bifurcationjump behaviour

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear systems in control theory (93C10) Bifurcations and instability for nonlinear problems in mechanics (70K50) Stochastic stability in control theory (93E15) Ordinary differential equations and systems with randomness (34F05) Control/observation systems governed by ordinary differential equations (93C15) Local and nonlocal bifurcation theory for dynamical systems (37G99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

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A new Markov selection procedure for degenerate diffusions ⋮ On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations ⋮ Stochastic bifurcation ⋮ Stochastic bifurcation ⋮ Analysis of emitter-coupled multivibrators by singularly perturbed systems ⋮ Simultaneous small noise limit for singularly perturbed slow-fast coupled diffusions ⋮ Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view

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