Impact ionization and intervalley electron scattering in InSb and InAs induced by a single terahertz pulse.

Electronic properties of InSb and InAs are sensitive to electric field due to their narrow forbidden energy gaps and big difference in effective masses of electrons in different conduction band valleys. Here we report impact ionization processes and redistribution of electrons between the Γ, L and X valleys induced by a single ultrashort terahertz (THz) pulse at 80 K temperature. Monte Carlo simulation revealed that electron motion in this case has near ballistic character. The threshold electric field of impact ionization increases as the THz pulse gets shorter, and the process of impact ionization essentially raises cooling rate of hot electrons. The L valley gets mainly occupied by electrons in InSb while the X valley holds the majority of electrons in InAs at strong electric fields, respectively above 20 kV/cm and 90 kV/cm. The calculated results are in good agreement with the available experimental data.

Stabilization of steady states in an array of all-to-all coupled oscillators.

An array of globally all-to-all coupled FitzHugh-Nagumo-type oscillators is considered. We suggest an adaptive first-order stable filter control feedback technique to stabilize the steady states of the oscillators. The overall system includes separate networks of coupling and control. Therefore, the controller does not depend on the intrinsic parameters of coupling between the oscillators. We have investigated stabilization of the steady states in an array of nonidentical oscillators analytically, numerically, and experimentally.

Enhanced control of saddle steady states of dynamical systems.

An adaptive feedback technique for stabilizing a priori unknown saddle steady states of dynamical systems is described. The method is based on an unstable low-pass filter combined with a stable low-pass filter. The cutoff frequencies of both filters can be set relatively high. This allows considerable increase in the rate of convergence to the steady state. We demonstrate numerically and experimentally that the technique is robust to the influence of unknown external forces, which change the position of the steady state in the phase space. Experiments have been performed using electrical circuits imitating the damped Duffing-Holmes and chaotic Lindberg systems.

Stabilizing saddles.

A synergetic control technique for stabilizing a priori unknown saddle steady states of dynamical systems is described. The method involves an unstable filter technique combined with a derivative feedback. The cut-off frequency of the filter is not limited by the damping of the system, and therefore can be set relatively high. This essentially increases the rate of convergence to the steady state. The synergetic technique is robust to the influence of unknown external forces, which change the coordinates of the steady state in the phase space.

Stabilization of saddle steady states of conservative and weakly damped dissipative dynamical systems.

An adaptive feedback method for tracking and stabilizing unknown and/or slowly varying saddle-type steady states of conservative and weakly damped dissipative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. The proposed controller involves both filters working in parallel. As a specific example, the Lagrange point L2 of the Sun-Earth system is discussed and the second-order saddle model is considered. Analog simulations have been performed using an inclusive nonlinear electrical circuit, imitating dynamics of a body along the Sun-Earth line. External chaotic perturbations have been used to check the robustness of the control technique.

Switching from stable to unknown unstable steady states of dynamical systems.

We demonstrate that a dynamical system can be switched from a stable steady state to a previously unknown unstable (saddle) steady state using proportional feedback coupling to an auxiliary unstable system. The simplest one-dimensional nonlinear model is treated analytically, the more complicated two-dimensional pendulum is considered numerically, while the damped Duffing-Holmes oscillator is investigated analytically, numerically, and experimentally. Experiments have been performed using a simplified version of the electronic Young-Silva circuit imitating the dynamical behavior of the Duffing-Holmes system. The physical mechanism behind the switching effect is discussed.