52,000 research outputs found
Rate of Decay of Stable Periodic Solutions of Duffing Equations
In this paper, we consider the second-order equations of Duffing type. Bounds
for the derivative of the restoring force are given that ensure the existence
and uniqueness of a periodic solution. Furthermore, the stability of the unique
periodic solution is analyzed; the sharp rate of exponential decay is
determined for a solution that is near to the unique periodic solution.Comment: Key words: Periodic solution; Stability; Rate of deca
Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities
We study the stability and exact multiplicity of periodic solutions of the
Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such
that the equation has exactly three ordered T-periodic solutions. Moreover,
when h is within these bounds, one of the three solutions is negative, while
the other two are positive. The middle solution is asymptotically stable, and
the remaining two are unstable.Comment: Keywords: Duffing equation; Periodic solution; Stabilit
Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type
We consider a second-order equation of Duffing type. Bounds for the
derivative of the restoring force are given which ensure the existence and
uniqueness of a periodic solution. Furthermore, the unique periodic solution is
asymptotically stable with sharp rate of exponential decay. In particular, for
a restoring term independent of the variable , a necessary and sufficient
condition is obtained which guarantees the existence and uniqueness of a
periodic solution that is stable.Comment: Key words and phrases: Periodic solution, topological degree,
stabilit
Quantization Errors of fGn and fBm Signals
In this Letter, we show that under the assumption of high resolution, the
quantization errors of fGn and fBm signals with uniform quantizer can be
treated as uncorrelated white noises
Inflation with Holographic Dark Energy
We investigate the corrections of the holographic dark energy to inflation
paradigm. We study the evolution of the holographic dark energy in the
inflationary universe in detail, and carry out a model-independent analysis on
the holographic dark energy correction to the primordial scalar power spectrum.
It turns out that the corrections generically make the spectrum redder. To be
consistent with the experimental data, there must be a upper bound on the
reheating temperature. We also discuss the corrections due to different choices
of the infrared cutoff.Comment: 15 pages, 3 figures, v2: references added, a fast-roll discussion
added. v3: typos corrected. v4: final version to appear in NP
Response to Comments on PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances
In this response, we try to give a repair to our previous proof for PCA Based
Hurst Exponent Estimator for fBm Signals by using orthogonal projection.
Moreover, we answer the question raised recently: If a centered Gaussian
process admits two series expansions on different Riesz bases, we may
possibly study the asymptotic behavior of one eigenvalue sequence from the
knowledge on the asymptotic behaviors of another.Comment: This is a response for a mistake in Li Li, Jianming Hu, Yudong Chen,
Yi Zhang, PCA based Hurst exponent estimator for fBm signals under
disturbances, IEEE Transactions on Signal Processing, vol. 57, no. 7, pp.
2840-2846, 200
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