Invariant Measures and Lyapunov Exponents for Stochastic Mathieu System
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- Type
- article
- Published
- 2002-12-01
- Cited by
- 21
- References
- 14
- OpenAlex
- https://openalex.org/W86700851
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:84181001
Keywords
Lyapunov exponent, Mathematics, Instability, Amplitude, Excitation
References
- Stochastic Stability of Differential Equations
- Introduction To Perturbation Techniques
- Multiple time scaling of the response of a Duffing oscillator to narrow-band random excitation
- Response statistics of non-linear systems to combined deterministic and random excitations
- Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems
- Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and application
- PRINCIPAL RESPONSE OF DUFFING OSCILLATOR TO COMBINED DETERMINISTIC AND NARROW-BAND RANDOM PARAMETRIC EXCITATION
- Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation
- Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion
- Invariant measures and Lyapunov exponents for generalized parameter fluctuations
- A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systems
- Topics in the theory of random noise
- Table of Integrals, Series, and Products.
- Stability of Linear Differential Systems with Parametric Excitation
- Qualitative Theory of Stochastic Systems
Cited by
- PARAMETRICALLY-EXCITED MICROELECTROMECHANICAL OSCILLATORS WITH FILTERING CAPABILITIES
- Implementation of Periodicity Ratio in Analyzing Nonlinear Dynamic Systems : A Comparison With Lyapunov Exponent
- Stochastic Stability of Damped Mathieu Oscillator Parametrically Excited by a Gaussian Noise
- Stability of an autoparametric pendulum system with impacts
- A molecular dynamics simulation study on trapping ions in a nanoscale Paul trap
- Stochastic rotational response of a parametric pendulum coupled with an SDOF system
- Saturation and resonance of nonlinear system under bounded noise excitation
- Largest Lyapunov exponent for second-order linear systems under combined harmonic and random parametric excitations
- Energy Response Probability Density Function of a Rotating Parametric Pendulum
- Stochastic stability of the non-homogeneous damped Mathieu equation
- Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation
- The fastest, simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems
- Reliability of electrostatically actuated MEMS resonators to random mass disturbance
- Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations
- The fastest, simplified method of estimation of the largest Lyapunov exponent for continuous dynamical systems with time delay
- Diagnosis and Control of Nonlinear Oscillations of a Fluttering Plate
- Molecular dynamics simulation study on trapping ions in a nanoscale Paul trap
- Characteristics Diagnosis of Nonlinear Dynamical Systems
- Rotating potential of a stochastic parametric pendulum
- Nonlinear Behaviour Diagnosis for Horizontal-Axis Wind Turbine Blades Subjected to Inconstant Wind Excitations
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