scholarly journals Compact attractors of an antithetic integral feedback system have a simple structure

2019 ◽  
Author(s):  
Michael Margaliot ◽  
Eduardo D. Sontag
Keyword(s):  
Controller Design ◽  
Feedback System ◽  
Dimensional System ◽  
Two Dimensional ◽  
Experimental Systems ◽  
System A ◽  
Dynamical Behaviors ◽  
Omega Limit Set ◽  
Open Question ◽  
Bounded Trajectory

AbstractSince its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional linear system (making the closed-loop system a nonlinear four-dimensional system) has been analyzed in much detail. This system has a unique equilibrium but, depending on parameters, it may exhibit periodic orbits. An interesting open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. This note shows that, for any parameter choices, every bounded trajectory satisfies a Poincaré-Bendixson property. The analysis is based on the recently introduced notion of k-cooperative dynamical systems. It is shown that the model is a strongly 2-cooperative system, implying that the dynamics in the omega-limit set of any precompact solution is conjugate to the dynamics in a compact invariant subset of a two-dimensional Lipschitz dynamical system, thus precluding chaotic and other strange attractors.

scholarly journals LOCALIZATION IN A STRONGLY DISORDERED SYSTEM: A PERTURBATION APPROACH

2013 ◽  
Vol 27 (13) ◽  
pp. 1350051
Author(s):  
MARCO FRASCA
Keyword(s):  
Scaling Law ◽  
Localization Length ◽  
Perturbation Approach ◽  
Dimensional System ◽  
Two Dimensional ◽  
Disordered System ◽  
System A ◽  
Large Perturbation ◽  
Two Dimensional System ◽  
Diagonal Disorder

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent ν = 1 in agreement with the Chayes criterion ν ≥ 1. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.

Coexistent multiple-stability of a fractional-order delayed memristive Chua’s system based on describing function

2020 ◽  
Vol 34 (14) ◽  
pp. 2050146
Author(s):  
Dawei Ding ◽  
Jun Luo ◽  
Xiangyu Shan ◽  
Yongbing Hu ◽  
Zongli Yang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Feedback System ◽  
Chua’S Circuit ◽  
Nonlinear Feedback ◽  
Describing Function ◽  
Chua's Circuit ◽  
System A ◽  
Dynamical Behaviors ◽  
Low Pass ◽  
Multiple Stability

In this paper, in order to analyze the coexistent multiple-stability of system, a fractional-order memristive Chua’s circuit with time delay is proposed, which is composed of a passive flux-controlled memristor and a negative conductance as a parallel combination. First, the Chua’s circuit can be considered as a nonlinear feedback system consisting of a nonlinear block and a linear block with low-pass properties. In the complex plane, the nonlinear element of the system can be approximated by a variable gain called a describing function. Second, compared with conventional computation, the describing function can accurately predict the hidden dynamics, fixed points, periodic orbits, unstable behaviors of the system. By using this method, the full mapping of the system dynamics in parameter spaces is presented, and the coexistent multiple-stability of the system is investigated in detail. Third, using bifurcation diagram, phase diagram, time domain diagram and power spectrum diagram, the dynamical behaviors of the system under different system parameters and initial values are discussed. Finally, based on Adams–Bashforth–Moulton (ABM) method, the correctness of theoretical analysis is verified by numerical simulation, which shows that the fractional-order delayed memristive Chua’s system has complex coexistent multiple-stability.

scholarly journals Modelling Diffusion in a Physically Constrained System: A Numerical Approach

2016 ◽  
Vol 2 (1) ◽  
pp. 38-48
Author(s):  
Adam Jozefiak ◽  
Jim Zhang Hao Li
Keyword(s):  
Mathematical Model ◽  
Numerical Approach ◽  
Dimensional System ◽  
Two Dimensional ◽  
Hydraulic Systems ◽  
Experimental Conditions ◽  
Constrained System ◽  
Exponential Factor ◽  
System A ◽  
Geometrically Constrained

Diffusion has been described on a microscopic scale by Einstein as a probabilistic collision of particles. On a macroscale, diffusion has been thoroughly described by Fick’s laws. However, the solutions to Fick’s laws are limited to idealized physical systems. The aim of this experimental study is to provide a mathematical model for diffusion which incorporates both macroscopic and microscopic properties to effectively model diffusion in a geometrically constrained two-dimensional system. Based on macroscopic and microscopic properties, two-dimensional diffusion was modelled as a summation of equally probable paths of diffusion. The point source diffusion of hydrochloric acid in an arena with variable barrier dimensions was monitored continuously using a pH probe. The numerical solution of the mathematical model for each experimental condition was determined and the pre-exponential factor was fit to the measurements. The average pre-exponential value was determined for each experimental condition, and t-scores were calculated to compare the average pre-exponential values which were found to be statistically similar. This indicates that the proposed model is an accurate model as it predicts identical pre-exponential values between experimental conditions, accounting for all variants that it attempts to model. This model provides a bridge between the microscopic and macrcoscopic theoretical descriptions of diffusion that were independently postulated by Einstein and Fick. Applications of the model include the approximation of locations of leakage in hydraulic systems.

scholarly journals Fuzzy Control of DC-DC Converters with Input Constraint

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
D. Saifia ◽  
M. Chadli ◽  
S. Labiod ◽  
H. R. Karimi
Keyword(s):  
Fuzzy Control ◽  
State Feedback ◽  
Controller Design ◽  
Actuator Saturation ◽  
External Disturbance ◽  
Fuzzy Model ◽  
Feedback System ◽  
Input Constraint ◽  
Lyapunov Approach ◽  
System A

This paper proposes a method for designing fuzzy control of DC-DC converters under actuator saturation. Because linear control design methods do not take into account the nonlinearity of the system, a T-S fuzzy model and a controller design approach is used. The designed control not only handles the external disturbance but also the saturation of duty cycle. The input constraint is first transformed into a symmetric saturation which is represented by a polytopic model. Stabilization conditions for the state feedback system of DC-DC converters under actuator saturation are established using the Lyapunov approach. The proposed method has been compared and verified with a simulation example.

New Methods for Analyzing Water Pollutants

1982 ◽  
Vol 14 (4-5) ◽  
pp. 59-71 ◽  
Author(s):  
L H Keith ◽  
R C Hall ◽  
R C Hanisch ◽  
R G Landolt ◽  
J E Henderson
Keyword(s):  
Amino Acids ◽  
Gas Chromatography ◽  
Two Dimensional ◽  
Gas Chromatograph ◽  
New Class ◽  
New Methods ◽  
System A ◽  
Drinking Waters ◽  
Computer Controlled ◽  
Nitrogen Containing Compounds

Two new methods have been developed to analyze for organic pollutants in water. The first, two-dimensional gas chromatography, using post detector peak recycling (PDPR), involves the use of a computer-controlled gas Chromatograph to selectively trap compounds of interest and rechromatograph them on a second column, recycling them through the same detector again. The second employs a new detector system, a thermally modulated electron capture detector (TMECD). Both methods were used to demonstrate their utility by applying them to the analysis of a new class of potentially ubiquitous anthropoaqueous pollutants in drinking waters- -haloacetonitriles. These newly identified compounds are produced from certain amino acids and other nitrogen-containing compounds reacting with chlorine during the disinfection stage of treatment.

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

Sign in / Sign up

Export Citation Format

Share Document