Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing resonant approximation that accurately captures a simplified form long-term evolution of small initial data. Topics covered include turbulent regular motion, dynamical recurrences analogous to Fermi-Pasta-Ulam phenomena oscillator chains, relations between nonr...

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 ...

A driven anharmonic oscillator is described which exhibits period doubling and chaotic behavior. The measured behavior of the oscillator under successive period doublings is in quantitative agreement with a recent theory which describes the behavior of nonlinear systems. Both the scalirg and the convergence rate predicted by the theory are verified by the experiment. The oscillator also exhibit...

Superconducting boron-doped silicon is a promising material for integrated quantum devices. In particular, its low electronic density and moderate disorder make it suitable candidate the fabrication of large inductances with losses at microwave frequencies. We study experimentally electrodynamics superconducting thin layers using coplanar waveguide resonators, focusing on kinetic inductance, in...