Comparison of time-delayed feedback schemes for spatiotemporal control of chaos in a reaction-diffusion system with global coupling

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
O. Beck ◽  
A. Amann ◽  
E. Schöll ◽  
J. E. S. Socolar ◽  
W. Just
Author(s):  
Svetlana V. Gurevich

The dynamics of a single breathing localized structure in a three-component reaction–diffusion system subjected to time-delayed feedback is investigated. It is shown that variation of the delay time and the feedback strength can lead either to stabilization of the breathing or to delay-induced periodic or quasi-periodic oscillations of the localized structure. A bifurcation analysis of the system in question is provided and an order parameter equation is derived that describes the dynamics of the localized structure in the vicinity of the Andronov–Hopf bifurcation. With the aid of this equation, the boundaries of the stabilization domains as well as the dependence of the oscillation radius on delay parameters can be explicitly derived, providing a robust mechanism to control the behaviour of the breathing localized structure in a straightforward manner.


2010 ◽  
Vol 371 (1-3) ◽  
pp. 60-65 ◽  
Author(s):  
Haixiang Hu ◽  
Xiaochun Li ◽  
Zhiming Fang ◽  
Xu Fu ◽  
Lin Ji ◽  
...  

2018 ◽  
Vol 2018 ◽  
pp. 1-24
Author(s):  
Satoshi Kawaguchi

We consider the motion of a spot under the influence of chemotaxis. We propose a two-component reaction diffusion system with a global coupling term and a Keller-Segel type chemotaxis term. For the system, we derive the equation of motion of the spot and the time evolution equation of the tensors. We show the existence of an upper limit for the velocity and a critical intensity for the chemotaxis, over which there is no circular motion. The chemotaxis suppresses the range of velocity for the circular motion. This braking effect on velocity originates from the refractory period behind the rear interface of the spot and the negative chemotactic velocity. The physical interpretation of the results and its plausibility are discussed.


1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.


2021 ◽  
Vol 31 (3) ◽  
pp. 033118
Author(s):  
Margaret K. McGuire ◽  
Chase A. Fuller ◽  
John F. Lindner ◽  
Niklas Manz

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll

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