• The architecture of chaos oscillator should be similar to classical second order sine wave oscillator, e.g. LC or Wien-bridge based circuit. • The oscillator should not be higher than the third order system. • The circuit should be an autonomous oscillator. • The active unit should be linear and separated from the nonlinear element(s). • The nonlinear element should be single and simple, e.g....

In this paper, He’s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy. Keywords—He’s amplitude frequency formulation; Periodic solution; Nonlinear oscillator; Fractional potential.

We show that nonlinear response of a quantum oscillator displays antiresonant dips as the field frequency passes adiabatically through multiphoton resonance. This coherent quantum effect has no analog in two-level systems. Its emergence is a consequence of special symmetry of a weakly nonlinear oscillator. We discuss the possibility to observe the antiresonance and the associated multiphoton Ra...

An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the f...

The amplitude–frequency relationship is an important mathematical property for a nonlinear oscillator. He’s amplitude–frequency formulation and the Max–Min approach are used to handle the conservative nonlinear oscillator ẍ +  1 + ẋ2  x = 0 for the amplitude–frequency relationship. The obtained result is compared with those in the open literature, revealing the effectiveness of the used metho...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

in this paper, solution of nonlinear optimal control problems and the controlled duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. this algorithm is based on state parametrization as a polynomial with unknown coefficients. by this method, the control and state variables can be approximated as a function of time. also, the ...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

A simple relaxation oscillator is designed by directly coupling a RC timing network to a passive S-shaped current-controlled nonlinear resistor and is then modified for chaos. The resulting chaotic oscillator inherits the main features of the relaxation oscillator, which are its low-power consumption and low-voltage operation from single or dual power supplies. These features are attributed to ...