# E. R. Hunt's research while affiliated with Ohio University and other places

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## Publications (20)

IntroductionThe OPF Method Circuit ImplementationControlling the Diode ResonatorControlling Coupled Diode Resonators On Higher Dimensional ControlControlling Spatiotemporal Chaos Open Flow SystemsThe Diode Resonator Open Flow SystemControlConclusions Circuit ImplementationControlling the Diode Resonator On Higher Dimensional Control Open Flow Syste...

We expand on prior results on noise supported signal propagation in arrays of
coupled bistable elements. We present and compare experimental and numerical
results for kink propagation under the influence of local and global
fluctuations. As demonstrated previously for local noise, an optimum range of
global noise power exists for which the medium a...

We investigate the response of a linear chain of diffusively coupled diode resonators under the influence of thermal noise. We also examine the connection between spatiotemporal stochastic resonance and the presence of kink-antikink pairs in the array. The interplay of nucleation rates and kink speeds is briefly addressed. The experimental results...

We establish the constructive role of noise on the signal transmission properties of spatially extended, metastable media. Our results are for an experimental system comprised of coupled, nonlinear resonators. The system's capability of reliable signal propagation is enhanced over a finite noise range. We briefly address the reliability of signal d...

This paper reviews recent advances in the application of chaos control techniques to the stability analysis of two-dimensional dynamical systems. We demonstrate how the system's response to one or multiple feedback controllers can be utilized to calculate the characteristic multipliers associated with an unstable periodic orbit. The experimental re...

A variety of spatial patterns embedded within an underlying spatiotemporally chaotic state is stabilized via various methods of boundary control. Results are presented for an experimental system consisting of unidirectionally coupled diode resonator circuits as well as for a coupled map lattice. Spatiotemporal chaos is eliminated either by locking...

We demonstrate the successful control of a periodic orbit associated with two unstable manifolds in a system comprised of two coupled diode resonators. It is shown that due to symmetries generic to spatially extended systems a one-parameter control is not possible. A novel method of determining the local Liapunov exponents utilizing orthogonal cont...

The phenomenon of array enhanced stochastic resonance is demonstrated in a system of coupled diode resonators. We present experimental evidence that the signal-to-noise ratio (SNR) of the output signal of a single diode resonator can be significantly improved by coupling it diffusively into an array of up to 32 non-identical oscillators. It is show...

We investigate the origin of stable spatially extended waveforms in an open flow system consisting of unidirectionally coupled chaotic oscillators. Results are obtained for an experimental system consisting of coupled diode resonators as well as for a coupled map lattice, a numerical model comprised of logistic maps. Under the conditions studied, s...

If one changes the control parameter of a chaotic system proportionally to the distance between an arbitrary point on the strange attractor and the actual trajectory, the lifetime τ of the most stable unstable periodic orbit in the vicinity of this point starts to diverge with a power law. The volume in parameter space where τ becomes infinite is f...

With various methods we demonstrate the establishment of stable, spatially extended wave forms underlying a spatiotemporally chaotic state in open flow systems consisting of coupled oscillators. Results are obtained for an experimental system consisting of unidirectionally coupled diode resonator circuits as well as for the coupled map lattice, a n...

The atomic and electronic structures of the 4Hb polytype (alternating layers of T and H types) of TaS2 have been studied with a scanning tunneling microscope, operating in air at room temperature. On areas with presumably the T-type layer being the surface, a commensurate √13×√13 charge-density wave (CDW) superlattice is observed, independent of sa...

Experimentally demonstrates that Chua's circuit, operating in the
double-scroll chaotic regime, may be brought to either of the two
unstable, stationary state fixed points by means of derivative control

The use of electronic circuits in studying chaotic dynamics and control are reviewed. Since all chaotic systems have several properties in common, simple circuits are analogous to much more complicated ones, such as lasers. Consequently, the methods developed to control chaos in electronic circuits are applicable to many diverse physical systems. T...

A scanning tunneling microscope (STM), operating in air at room temperature, has been used to study the charge-density waves (CDW’s) on the surface of 1T-TaS2 with many different Pt/Ir, W, Ni, and Co tips. Images of CDW’s with strong atomic modulation, as well as those with weakly superimposed atomic modulation, have been observed with all differen...

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua’s circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbit...

A scanning tunneling microscope, operating in air at room temperature, has been used to study the surface of 2H-TaS2 intercalated with Ag. A new 2×1 superlattice has been observed in regions of the stage-2 compound. In other regions the hexagonal images are the same as those of pure 2H-TaS2. The 2×1 superlattice is believed to be associated with re...

The surfaces of the CuCl2 graphite intercalation compounds (GIC's), uniform stage 1, were investigated in air using a scanning tunneling microscope. The carbon site asymmetry observed in STM images of pristine graphite is absent in the images of these GIC samples. For all samples we find no evidence for the STM bias voltage polarity affecting the i...

A multimode, autonomously chaotic solid-state laser system has been controlled by the technique of occassional proportional feedback, related to the control scheme of Ott, Grebogi, and Yorke. We show that complex periodic wave forms can be stabilized in the laser output intensity. A detailed model of the system is not necessary. Our results indicat...

## Citations

... Meanwhile, the OGY method and modifications of it have been applied to a multitude of mathematical and physical systems. Examples are as diverse as the stabilisation of a parametrically excited cantilever ribbon [192], of higher-order periodic orbits in a periodically driven diode resonator [207,208] and other electronic circuits [209], of periodic orbits in chemical system [210][211][212] such as the control of chaos in the Belousov-Zhabotinsky reaction [212], the stabilisation of complex periodic waveforms of a chaotic multi-mode laser [213][214][215], the suppression of chaotic flow in a thermal convection loop [216] and in a microwave-pumped spinwave-instability experiment [217], and stabilisation of cardiac arrhythmia [93,218]. Meanwhile, also Hamiltonian systems with complex conjugated eigenvalues can be stabilised employing the OGY method [180][181][182] (for more applications, see Ref. [183] and references therein). ...

... Kadar et al. found that wave transmission in a photosensitive Belousov-Zhabotinsky chemical reaction is enhanced by increasing noise strength, and sustained transmission is achieved at an optimal noise strength [25]. Locher et al. investigated the noise effect on signal transmission in a metastable medium and discovered that noise can improve signal transmission [26]. Gammaitoni et al. examined signal transmission in a unidirectional coupled bistable system with uncorrelated noise and determined the optimal noise strength for the largest signal transmission distance and optimal response [27]. ...

... It adds some difficulty to the understanding of the appearance/disappearance mechanisms of chaotic behavior [1]. Therefore the shift of focus from single-to multi parameter case [2][3][4][5] is the natural continuation of the studies in the field of the analysis of the controlled processes, taking place in chaotic systems. ...

... In spite of a careful selection, the drive voltage for a given feature, such as the period-3 fixed points, varies by up to 20% between basic elements. This one-dimensional setup has been previously studied with unidirectional coupling [7] and under the conditions of stochastic resonance [8,9,10]. ...

... Apparently, only part of the intercalated Cu is ordered at RT, while the rest remains disordered. Several previous STM studies of intercalated transition metal dichalcogenides [11,14,18] have raised the possibility of the existence of induced surface CDWs in these compounds. Since the 2H a polytype of NbSe 2 was reported to exhibit a CDW with a 3a 0 Â 3a 0 superstructure at 33 K, a similar behavior might be expected in the isostructural 2H a ±NbS 2 . ...

... † Corresponding authors: xluo@issp.ac.cn ‡ wjlu@issp.ac.cn § ypsun@issp.ac.cn (ICCDW) at T ICCDW ∼ 550 K, a nearly commensurate CDW (NCCDW) at T NCCDW ∼ 350 K, and a commensurate CDW (CCDW) at T CCDW ∼ 180 K, which is believed to be driven by strong electronic correlations and electron-phonon coupling [10][11][12]. Especially, the emergent CDW pattern has been observed below T CCDW , where all Ta atoms form a superstructure that assumes √ 13 × √ 13, the so-called David star arrangement, which has been confirmed by different experimental probes and calculations [13,14]. The macroscopic resistance measurement of it shows that when the CDW occurs, the resistance rises sharply with obvious hysteresis, indicating the phase transition. ...

... In contrast to the low-temperature insulating phase in bulk 1T -TaS 2 , 4H b -TaS 2 is a superconductor with transition temperature T c ∼ 3 K (see Supplemental Materials S1, [19]). Although the √ 13 × √ 13 CDW order exists in the 1T -TaS 2 layer of 4H b -TaS 2 , the CDW order in the 1H-TaS 2 layer of 4H b -TaS 2 is very weak [20][21][22]. The 1H-TaS 2 layer in 4H b -TaS 2 can greatly reduce the interlayer CDW coupling between the adjacent 1T -TaS 2 layers in 4H b -TaS 2 , and the previous ARPES measurements indicate 1T -TaS 2 and 1H-TaS 2 layers still retain their original electronic dispersion [23]. ...

... Hunt et al. presented experimental evidence that the SNR of a single-diode resonator can be improved by coupling the resonator diffusively to an array of up to 32 non-identical resonators. The group also presented analytical results for the synchronization and signal processing properties of 4 field theory and explored the effects of various forms of nonlinear coupling [21][22][23][24]. Except for the research showing that noise can effectively enhance the output SNR in coupled and spatially extended systems, recent studies have demonstrated that noise can support or sustain signal propagation in various numerical and experimental coupled nonlinear systems; this phenomenon can be understood as a generalization of SR to spatially extended systems [25][26][27]. ...

... The concept of controlling chaos, referred to as the OGY method, was first proposed by Ott et al. [11], and multiple studies on controlling chaos have been reported [12,13]. Controlling chaos in lasers has been experimentally achieved [14], and chaotic oscillations in lasers can be stabilized into steadystate or periodic outputs. Techniques for controlling chaos in lasers have been applied for the stabilization of chaos into high periodic oscillations [15], suppression of relative intensity noise [16], and dynamic associative memory [17]. ...

... The motivation to explore noise-induced complex behavior in coupled systems arises from the observation that Brownian particles do not always work independently but operate in groups and form coupled systems [15][16][17][18]; thus, coupling should be considered to explore new dynamical features and cooperative behavior in such coupled systems. The important phenomena of couplingenhanced SR and coupling-induced cooperative behavior in coupled models have been demonstrated [19][20][21][22][23][24]. Furthermore, several studies have demonstrated that noise can support or sustain signal transmission in various numerical and experimental coupled systems. ...