AI Article Synopsis
- The state-space-split method has been expanded to tackle generalized Fokker-Planck-Kolmogorov equations in high-dimensional stochastic dynamical systems, focusing on polynomial nonlinearities and Poissonian white noise.
- The analysis specifically examines the behavior of a stretched Euler-Bernoulli beam with cubic nonlinearity affected by uniformly distributed Poissonian white noise using this new solution procedure.
- Numerical results indicate that the state-space-split method, combined with the exponential polynomial closure method, provides results that closely match those from Monte Carlo simulations under certain conditions regarding system relaxation time and Poisson impulse arrival time.
Article Abstract
The state-space-split method for solving the Fokker-Planck-Kolmogorov equations in high dimensions is extended to solving the generalized Fokker-Planck-Kolmogorov equations in high dimensions for stochastic dynamical systems with a polynomial type of nonlinearity and excited by Poissonian white noise. The probabilistic solution of the motion of the stretched Euler-Bernoulli beam with cubic nonlinearity and excited by uniformly distributed Poissonian white noise is analyzed with the presented solution procedure. The numerical analysis shows that the results obtained with the state-space-split method together with the exponential polynomial closure method are close to those obtained with the Monte Carlo simulation when the relative value of the basic system relaxation time and the mean arrival time of the Poissonian impulse is in some limited range.
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| http://dx.doi.org/10.1103/PhysRevE.85.067701 | DOI Listing |
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Article Synopsis
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