Abstract: A cyclostationary Gaussian linearization method is
formulated for investigating the time average response of nonlinear
system under sinusoidal signal and white noise excitation. The
quantitative measure of cyclostationary mean, variance, spectrum of
mean amplitude, and mean power spectral density of noise are
analyzed. The qualitative response behavior of stochastic jump and
bifurcation are investigated. The validity of the present approach in
predicting the quantitative and qualitative statistical responses is
supported by utilizing Monte Carlo simulations. The present analysis
without imposing restrictive analytical conditions can be directly
derived by solving non-linear algebraic equations. The analytical
solution gives reliable quantitative and qualitative prediction of mean
and noise response for the Duffing system subjected to both sinusoidal
signal and white noise excitation.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.