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 inv...

Consider the stochastic Duffing-van der Pol equation ẍ = −ω2x− Ax −Bx2ẋ + εβẋ + εσxẆt with A ≥ 0 and B > 0. If β/2 + σ/8ω > 0 then for small enough ε > 0 the system (x, ẋ) is positive recurrent in R \ {0}. Let λ̃ε denote the top Lyapunov exponent for the linearization of this equation along trajectories. The main result asserts that λ̃ε ∼ ελ̃ as ε → 0 where λ̃ is the top Lyapunov exponent along tra...

Nonlinear oscillators with hardening and softening cubic Duffing nonlinearity are considered. Such classical conservative oscillators are known to have an amplitude-dependent period. In this work, we design oscillators with the Duffing-type restoring force but an amplitude-independent period. We present their Lagrangians, equations of motion, conservation laws, as well as solutions for motion.

We have studied experimentally the inverse system approach, which is used when we want to synchronize two chaotic systems (master – slave). We apply this method to a second order nonlinear circuit, which is described by a Duffing equation. We present two different implementations of the slave circuit with the inverse method and we demonstrate the possibility of synchronization when the two circ...

In this paper introducing novel mathematical approach to reduce the computational effort of non-linear problems and the technique called as novel technique. In this paper solve the Duffing and Duffing-Holmes equations by using novel technique is described clearly. This method consists of decomposing a given differential equation in to linear, non-linear and remainder terms. The method has been ...

An asymptotically stable direct adaptive fuzzy PI sliding modecontroller is proposed for a class of nonlinear uncertain systems. In contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.Moreover, a PI control structure is used to attenuate chattering. The approachis applied to stabilize an open-...

poly (propylene fumarate) (ppf), a linear unsaturated polyester consisting of alternating propylene glycol and fumaric acid units, can be cured in vivo to fill the skeletal defects with minimal surgical intervention. many different methods have been reported for synthesizing ppf, but none of them gives a clear method. the present paper introduces two new methods in ppf synthesis: modified reflu...

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Mor...

In this work, we propose a novel phenomenological model of the EEG signal based on the dynamics of a coupled Duffing-van der Pol oscillator network. An optimization scheme is adopted to match data generated from the model with clinically obtained EEG data from subjects under resting eyes-open (EO) and eyes-closed (EC) conditions. It is shown that a coupled system of two Duffing-van der Pol osci...