Experimental Demonstration of Antimonotonicity: The Concurrent Creation and Destruction of Periodic Orbits in a Driven Nonlinear Electronic Resonator

Flux bias-controlled chaos and extreme multistability in SQUID oscillators

The radio frequency (rf) Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator exhibiting the rich dynamical behavior. It has been studied for many years and it has found numerous applications in magnetic field sensors, in biomagnetism, in non-destructive evaluation, and gradiometers, among others. Despite its theoretical and practical importance, there is relatively very little work on its multistability, chaotic properties, and bifurcation structure. In the present work, the dynamical properties of the SQUID in the strongly nonlinear regime are demonstrated using a well-established model whose parameters lie in the experimentally accessible range of values. When driven by a time-periodic (ac) flux either with or without a constant (dc) bias, the SQUID exhibits extreme multistability at frequencies around the (geometric) resonance. This effect is manifested by a "snake-like" form of the resonance curve. In the presence of both ac and dc flux, multiple bifurcation sequences and secondary resonance branches appear at frequencies above and below the geometric resonance. In the latter case, the SQUID exhibits chaotic behavior in large regions of the parameter space; it is also found that the state of the SQUID can be switched from chaotic to periodic or vice versa by a slight variation of the dc flux.

Hurst exponents and cyclic scenarios in a photonic integrated circuit

We experimentally report the cyclic scenario of birth and annihilation of periodic orbits in a photonic integrated circuit as the feedback phase of the electric field varies. The latter is also shown to result in minimal alterations in the statistical properties of the chaotic attractor, with simultaneously transiting the Hurst exponent H , erratically, below and above the critical value of H=0.5 that indicates regular Brownian motion. Consequently there is an indication of the most effective operating regions with minimized predictability, which hinders eavesdropping and the progress of forecasting the development of the chaotic light carrier.

Stabilizing unstable steady states using extended time-delay autosynchronization

We describe a method for stabilizing unstable steady states in nonlinear dynamical systems using a form of extended time-delay autosynchronization. Specifically, stabilization is achieved by applying a feedback signal generated by high-pass-filtering in real time the dynamical state of the system to an accessible system parameter or variables. Our technique is easy to implement, does not require knowledge of the unstable steady state coordinates in phase space, automatically tracks changes in the system parameters, and is more robust to broadband noise than previous schemes. We demonstrate the controller's efficacy by stabilizing unstable steady states in an electronic circuit exhibiting low-dimensional temporal chaos. The simplicity and robustness of the scheme suggests that it is ideally suited for stabilizing unstable steady states in ultra-high-speed systems. (c) 1998 American Institute of Physics.