A simple adaptive controller based on a low-pass filter to stabilize unstable steady states of dynamical systems is considered. The reference-free; it does not require knowledge the location fixed point in phase space. topological limitation similar that delayed feedback discussed. We show saddle-type cannot be stabilized by using conventional filter. can overcome an use demonstrated for several physical models, including pendulum driven constant torque, Lorenz system, and electrochemical...

An adaptive dynamic state feedback controller for stabilizing and tracking unknown steady states of dynamical systems is proposed. We prove that the can never be stabilized if system in sum have an odd number real positive eigenvalues. For two-dimensional systems, this topological limitation only unstable focus or node with a stable controller, stabilization saddle requires presence degree freedom loop. The use to stabilize track points (as well as foci) demonstrated both numerically...

We develop an analytical approach for the delayed feedback control of Lorenz system close to a subcritical Hopf bifurcation. The periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by conventional technique. utilize modification based on unstable controller. employs center manifold theory near identity transformation. derive characteristic equation Floquet exponents controlled orbit in form obtain simple expressions threshold stability as well optimal value...

We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in dynamical system at subcritical Hopf bifurcation. Close to bifurcation point problem is treated analytically using method averaging. discuss necessity employing an degree freedom loop as well nonlinear coupling between controlled and controller. To demonstrate our analytical approach specific example electronic circuit taken model

We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free periodic orbits in nonautonomous chaotic systems. To improve global control performance we introduce a two-step algorithm. The problem of linear stability system under treated analytically. Theoretical results are confirmed by electronic circuit experiments forced double-well oscillator.

Describing the collective dynamics of large neural populations using low-dimensional models for averaged variables has long been an attractive task in theoretical neuroscience. Recently developed reduction methods make it possible to derive such directly from microscopic individual neurons. To simplify reduction, Cauchy distribution is usually assumed heterogeneous network parameters. Here we extend method a wider class heterogeneities defined by q-Gaussian distribution. The shape this...

A novel, very simple chaotic oscillator is described. It intended for training laboratories accompanying courses on nonlinear dynamics and chaos undergraduate, postgraduate PhD students. The consists of an operational amplifier, LCR resonance loop, extra capacitor, a diode as element three auxiliary resistors. Chaotic oscillations are demonstrated both experimentally numerically.

Act-and-wait modification of a time-delayed feedback control (TDFC) algorithm is proposed to stabilize unstable periodic orbits in nonautonomous dynamical systems. Due periodical switching on and off the perturbation, an infinite-dimensional function space TDFC system reduced finite-dimensional state space. As result number Floquet exponents defining stability controlled orbit remains same as for control-free system. The values these can be effectively manipulated by variation parameters. We...

A modified delayed feedback control algorithm with the improved global properties is proposed. The modification based on ergodic features of chaotic systems. We do not perturb system until its state approaches a desired unstable periodic orbit and then we activate force. To evaluate closeness to target orbit, special devised. For continuous-time systems, it can be implemented by means simple low-pass filter. An additional filter used for selection particular from several orbits same period.

In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed new chaos control method in which target periodic orbit is approximated by system of harmonic oscillators. We consider an application such controller to single-input single-output systems the limit infinite number By evaluating transfer function this limit, we show that transforms into known extended time-delayed feedback controller. This finding gives rise approximate finite-dimensional theory algorithm, provides...

The considered chaotic oscillator consists of an amplifier, 2nd order LC resonator, Schottky diode and extra capacitor in parallel to the diode.The plays role a nonlinear device.Chaotic oscillations are demonstrated numerically experimentally at low as well high megahertz frequencies, up 250 MHz.

We devise a modified delayed feedback control algorithm that allows one to stabilize unstable target states of chaotic systems for any initial conditions placed on strange attractor.The is based ergodicity systems.We first let the system evolve unperturbed until it approaches neighbourhood state.Then we activate controller stabilizes state.We propose special evaluates closeness current state state.For continuous-time systems, this can be implemented by simple low-pass filters.We demonstrate...

The results of a study irreversible damage induced in microstrips made from high-T/sub c/ thin films by high-power electromagnetic pulses is presented. It was demonstrated that at high supercritical currents, the magnetic flux flow process induces fast thermomagnetic instability. result this instability local propagation, and subsequent film. parameter D=(I/sub d/-I/sub c/)/I/sub c/, where I/sub d/ are critical damaging superconducting-to-dissipative state transition respectively, which...

We derive mean-field equations for a large population of globally coupled quadratic integrate-and-fire neurons subject to weak Gaussian noise and heterogeneous time-independent non-Cauchy distributed currents. employ circular cumulant approach that has previously been used only in the context Cauchy heterogeneity, best our knowledge. extend this rational distribution functions, which, unlike function, can have many poles complex plane. Population dynamics are analyzed two families functions...