Bifurcation search via feedback loop breaking in biochemical signaling pathways with time delay

Waldherr, Steffen; Dylus, David; Allgöwer, Frank

doi:10.1002/asjc.383

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…Our method takes in particular the network topology into account during the fixed point calculation and analysis. This approach is very related to the so-called loop breaking approach presented in Waldherr and Allgöwer (2009);Waldherr et al (2011) for biochemical network models with and without time delays. Here the authors also use the idea of investigating stability properties of fixed points via breaking feedback loops in the system.…”

Section: Resultsmentioning

confidence: 99%

Bifurcation Analysis for Intracellular Regulation Networks Based on Their Circuit Structure

Radde

Klaus

2015

IFAC-PapersOnLine

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In earlier work we have developed the circuit-breaking algorithm. This algorithm uses the topology of a dynamic model for a regulatory network to construct a one-dimensional circuitcharacteristic. Zeros of this characteristic correspond to the fixed points of the system. Here we use the circuit-breaking algorithm as a tool to identify feedback circuits that are responsible for fixed point bifurcations, which are a main source of complex dynamic behavior. The methods are applied to and evaluated with two biological network models, a simplified regulatory network for a switch with three interconnected positive circuits, and a more complex network for cell cycle control in Xenopus frog eggs.

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Section: Resultsmentioning

confidence: 99%

Bifurcation Analysis for Intracellular Regulation Networks Based on Their Circuit Structure

Radde

Klaus

2015

IFAC-PapersOnLine

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“…Bifurcation phenomena happen in many industrial control domains. A method to locate bifurcations in time delay systems with a potentially high-dimensional parameter space, has been denoted in [1]. It can determine which parameters are relevant for complex dynamical behavior in such networks.…”

Section: Introductionmentioning

confidence: 99%

Measurement and Control of Magnetic Flux Signal in a Maglev System

Zhang¹,

Li²,

Zhang³

et al. 2013

Asian Journal of Control

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A linear model of the magnetic-levitation (maglev) system, including magnetic flux signal, has been established based on feedback linearization. This paper emphasizes measurements of magnetic flux signal and velocity signal, which are realized easily by electromagnetic induction law. The magnetic flux signal's range obtained by this method is wide. The degree of sensitivity can be regulated by changing the vertical area of the induction coils. Furthermore, this paper has designed a PIDB (proportion, integration, differentiation, flux density B) controller based on flux feedback, and some experiments have been performed on a CMS04 magnetic suspension vehicle in the national mid-low speed maglev experiment field of Tangshan city, China. The experimental results denote that the PIDB control method designed in this paper has more advantages than the traditional control method with position and current double cascades, and the robustness and stability of the maglev control system by this method have been verified effectively. in Wiley Online Library 165-175 815Guideway Electromagnet A Fig. 2. Simplified model of the maglev system.

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Section: Introductionmentioning

confidence: 99%

Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

Zhang

et al. 2013

Mathematical Problems in Engineering

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Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT) in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

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Bifurcation search via feedback loop breaking in biochemical signaling pathways with time delay

Cited by 3 publications

References 11 publications

Bifurcation Analysis for Intracellular Regulation Networks Based on Their Circuit Structure

Bifurcation Analysis for Intracellular Regulation Networks Based on Their Circuit Structure

Measurement and Control of Magnetic Flux Signal in a Maglev System

Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

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