Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation

DOI10.1016/J.CNSNS.2016.05.004zbMath1473.70053OpenAlexW2346858265MaRDI QIDQ2004787

Yanwen Xiao, Yahui Sun, Yongge Yang, Wei Xu

Publication date: 7 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2016.05.004

zbMATH Keywords

stochastic averaging methodfractional derivativestochastic bifurcationnon-smooth transformationvan der Pol vibroimpact system

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Impact in solid mechanics (74M20) Generation, random and stochastic difference and differential equations (37H10)

Related Items (14)

The stochastic P-bifurcation analysis of the impact system via the most probable response ⋮ A novel stochastic bifurcation and its discrimination ⋮ Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system ⋮ Resonance phenomenon for a nonlinear system with fractional derivative subject to multiplicative and additive noise ⋮ Stochastic response of a vibro-impact system with variable mass ⋮ Effect of fractional-damping and multiplicative colored noise on stochastic resonance for a second-order nonlinear system ⋮ Stochastic bifurcations of nonlinear vibroimpact system with time delay and fractional derivative excited by Gaussian white noise ⋮ Bifurcation Analysis of a Vibro-Impact Viscoelastic Oscillator with Fractional Derivative Element ⋮ Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller ⋮ Stability and bifurcation analysis of single-degree-of-freedom linear vibro-impact system with fractional-order derivative ⋮ Effect of the policy and consumption delay on the amplitude and length of business cycle ⋮ Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback ⋮ Probabilistic response of a fractional-order hybrid vibration energy harvester driven by random excitation ⋮ The stochastic bifurcation of the vibro-impact system on the impact surface via a new path integration method

Cites Work

• Unnamed Item
• Bifurcation control of bounded noise excited Duffing oscillator by a weakly fractional-order \(PI^{\lambda} D^{\mu}\) feedback controller
• Primary resonance of Duffing oscillator with fractional-order derivative
• Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise
• Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations
• Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
• Random vibrations of Rayleigh vibroimpact oscillator under parametric Poisson white noise
• Stochastic dynamics and fractional optimal control of quasi integrable Hamiltonian systems with fractional derivative damping
• Random vibrations with impacts: a review
• Corner bifurcations in nonsmoothly forced impact oscillators
• Double Neimark–Sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops
• SLIDING BIFURCATIONS: A NOVEL MECHANISM FOR THE SUDDEN ONSET OF CHAOS IN DRY FRICTION OSCILLATORS

This page was built for publication: Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation