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Sufficient conditions for almost sure stability conditions are obtained for both elastic and viscoelastic columns.
Now we give a main result of the almost sure stability of the approximate solution (2.1).
In what follows we introduce the result of almost sure stability of SDDEs (1.1).
Based on the largest Lyapunov exponent, the almost sure stability of the trivial steady-state solution is examined.
Analytical results for the almost sure stability of the inactive mode are obtained and compared with simulation results.
Generally, almost sure stability is less restrictive than moment stability, and almost sure stability results are more difficult to establish if deriving from the moment stability by the Chebyshev inequality and the Borel-Cantelli lemma.
Similar(39)
The definitions of almost-sure stability and mean-square stability and the corresponding stability theorems are presented.
These equations, along with their sample properties, are then examined to obtain the almost-sure stability conditions.
The almost-sure stability or instability of the stochastic system depends on the sign of the largest Lyapunov exponent.
A method for obtaining a sufficient almost-sure stability condition for second order linear systems with an ergodic stiffness coefficient is presented.
The maximal Lyapunov exponent is calculated using the ergodic scalar diffusive process, which in turn yields the almost-sure stability conditions.
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