Delay-induced wave instabilities in single-species reaction-diffusion systems.

Teleoperation system performance suffers from the delays in communication lines. These delays are usually variable time delays. The customary wave variable technique used for constant time delays cannot provide satisfactory results to stabilize the system under variable delays. Another problem is observed in the position tracking performance of the limited-workspace teleoperation systems. Although wave variable technique is proven to track position demands successfully under constant time delays given that there is no communication failure, position tracking performance also degrades under variable delays. In this paper, a new controller is proposed to stabilize the system and enhance position tracking performance under variable time delays. This proposed controller is then applied to an identical master-slave teleoperation configuration which qualifies as a limited-workspace teleoperation system.

We analyze the condition for instability and pattern formation in reaction-diffusion systems beyond the usual linear regime. The approach is based on taking into account perturbations of higher orders. Our analysis reveals that nonlinearity present in the system can be instrumental in determining the stability of a system, even to the extent of destabilizing one in a linearly stable parameter regime. The analysis is also successful to account for the observed effect of additive noise in modifying the instability threshold of a system. The analytical study is corroborated by numerical simulation in a standard reaction-diffusion system.

Signal correlator with programmable variable time delay based on optical coherent transients

Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the feedback loop. Design of the feedback controller is then followed. Furthermore, eigenvalue assignment for the input-delay system is also obtained as well. Numerical examples illustrate the procedure of assigning the desired eigenvalue.

In this paper, the problem of stability and tracking performance of FRVF (Forbidden Region Virtual Fixture) for bilateral nonlinear teleoperation systems is studied in presence of varying time delay. It is proved that PD-like controllers can stabilize the teleoperation systems with FRVF in slave side and variable time delay in communication channels. It is also proved by proposed Lyapunov-Krasovskii's function that the mentioned problem of stability and tracking performance of FRVF is satisfied. Finally, the proficiency of this approach is demonstrated by simulating the method on a pair of 6-DOF (Degree of Freedom) PHANToM Omni robots with nonlinear dynamics. Keywords— Virtual fixture; variable delay; delayed teleoperation system; nonlinear teleoperation.

Reaction-diffusion systems involving ionic species are susceptible to an externally applied electric field. Depending on the charges on the ionic species and the intensity of the applied electric field, diverse spatiotemporal patterns can emerge. We here considered two prototypical reaction-diffusion systems that follow activator-inhibitor kinetics: the photosensitive chlorine dioxide-iodine-malonic acid (CDIMA) reaction and the Brusselator model. By theoretical investigation and numerical simulations, we unravel how and to what extent an externally applied electric field can induce and modify the dynamics of these two systems. Our results show that both the uni- and bi-directional electric fields may induce Turing-like stationary patterns from a homogeneous uniform state resulting in horizontal, vertical, or bent stripe-like inhomogeneity in the photosensitive CDIMA system. In contrast, in the Brusselator model, for the activator and the inhibitor species having the same positive or negative charges, the externally applied electric field cannot develop any spatiotemporal instability when the diffusion coefficients are identical. However, various spatiotemporal patterns emerge for the same opposite charges of the interacting species, including moving spots and stripe-like structures, and a phenomenon of wave-splitting is observed. Moreover, the same signand different magnitudes of the ionic charges can give rise to Turing-like stationary patterns from a homogeneous, stable, steady state depending upon the intensity of the applied electric field in the case of the Brusselator model. Our findings open the possibilities for future experiments to verify the predictions of electric field-induced various spatiotemporal instabilities in experimental reaction-diffusion systems.

Internet-based teleoperation employs robots and internet a two breakthrough technologies to manipulate robots from distance for different applications. Variable and unknown time delay dynamics of internet is the main obstacle for realtime teleoperation via internet. In this paper the internet delay dynamics and its characteristics have been studied based on the measurement in different nodes. Then a black-box model for end-to-end internet delay dynamics has been developed using system identification and Auto-Regressive eXogeneous (ARX) model. Our experimental studies show a regular periodic behaviour in long-term intervals of internet delay variation and also confirm the accuracy and reliability of our theoretical and modelling derivations. This paper also introduces a novel multivariable control method for real-time telerobotic operations via Internet. Random communications delay of the Internet can cause instability in realtime closed-loop telerobotic systems. When a single identification model is used, it will have to adapt itself to the operating condition before an appropriate control mechanism can be applied. Slow adaptation may result in a large transient error. As an alternative, we propose to use a Multiple Model framework. The control strategy is to determine the best model for the current operating condition and activate the corresponding controller. We propose the use of Multi-Model Adaptive Control Theory and Multivariable Wave prediction method to capture the concurrency and complexity of Internet-based teleoperation. The results confirm the efficiency of the proposed technique in dealing with constant and variable delay dynamics of internet.

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction–diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to infty , gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh–Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.

Dynamic output-feedback-based [formula omitted] design for networked control systems with multipath packet dropouts

Will Israel and Jordan be likely to stave off Palestinian irredentism from the recently established Palestinian Authority? Will transnational Palestinian identity undermine a future regional order based on partition into sovereign territorial states? These questions may be crucial in determining whether the emerging repartition of Palestine/Israel and the creation of the Palestinian Authority in the aftermath of the Oslo peace agreement will be the culminating stage of a long process of transformation from a multinational Ottoman Empire into a stable territorial state system or the beginning of a new wave of instability and renewed division in the region. The article explores these questions by comparatively analyzing attitudinal studies of Palestinian citizens of Israel and Jordan towards their respective states, the other community, and the peace process to gauge the dangers of secessionism or irredentism of these two groups and their likely impact on regional order in the Middle East. The analysis is framed within the primordial-cultural/instrumental-rational actor debate. The willingness of these two groups to compromise primordial sentiment and preserve the territorial integrity of Israel and Jordan, and the fact that each group prefers a slightly different political outcome that conforms with their respective material interests seems to confirm the rational-actor approach, the viability of the partition approach between Israel and the Palestinian Authority, the low probability of secessionism on the part of these two groups, and the low probability of responding to irredentist pressures should the future Palestinian entity exert them.

Cooperative behaviors arising from bacterial cell-to-cell communication can\nbe modeled by reaction-diffusion equations having only a single diffusible\ncomponent. This paper presents the following three contributions for the\nsystematic analysis of Turing instability in such reaction-diffusion systems.\n(i) We first introduce a unified framework to formulate the reaction-diffusion\nsystem as an interconnected multi-agent dynamical system. (ii) Then, we\nmathematically classify biologically plausible and implausible Turing\ninstabilities and characterize them by the root locus of each agent's dynamics,\nor the local reaction dynamics. (iii) Using this characterization, we derive\nanalytic conditions for biologically plausible Turing instability, which\nprovide useful guidance for the design and the analysis of biological networks.\nThese results are demonstrated on an extended Gray-Scott model with a single\ndiffuser.\n

In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic stability of its equilibria and the phenomenon of Hopf bifurcation for this system are considered. Using the Liapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Furthermore, based on some knowledge of limit set, we show the necessary and sufficient conditions of permanent of the turbidostat model. Finally, numerical simulations are offered to support our results.

In a two-planet system, a topological boundary that is created by Sundman (1912, Acta Math., 36, 105) inequality can forbid close encounters between the two planets for an infinite time. A system is said to be Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extrasolar planet dynamics. However, the coplanar and circular orbit approximation is often used. In this paper, we explain how the Hill stability can be understood in the framework of angular momentum deficit (AMD). In the secular approximation, AMD allows us to discriminate between a priori stable systems and systems for which a more in-depth dynamical analysis is required. We show that the general Hill stability criterion can be expressed as a function of only semimajor axes, masses, and total AMD of the system. The proposed criterion is only expanded in the planets-to-star mass ratio ε and not in the semimajor axis ratio, eccentricities, nor the mutual inclination. Moreover, the expansion in ε remains excellent up to values of about 10−3 even for two planets with very different mass values. We performed numerical simulations in order to highlight the sharp change of behavior between Hill stable and Hill unstable systems. We show that Hill stable systems tend to be very regular, whereas Hill unstable systems often lead to rapid planet collisions. We also note that Hill stability does not provide protection from the ejection of the outer planet.

A trigonometric approximation scheme for optimal periodic control problems with state and control dependent delays is considered. The formulation of approximate problems is here adapted to a specific form of state equation with variable time delays. Sufficient conditions for the sequence of nearly optimal solutions of approximate problems to be a generalized minimizing sequence for the basic problem are given. The application of the method proposed to a periodic control of chemical reactors with recycles and controlled piping is pointed out.

Improved stabilization criteria for Takagi–Sugeno fuzzy systems with variable delays