Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation

Ma, Jun; Gao, Jungang; Wang, Chunni; Su, Junyan

doi:10.1016/j.chaos.2006.11.039

Cited by 26 publications

(7 citation statements)

References 16 publications

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“…Many evidences have confirmed that the spiral wave in cardiac tissue is responsible for one kind of heart disease, and instability of the spiral wave in cardiac tissue can cause rapid death of the heart. Therefore, it is interesting to study the control and removal of the spiral wave [7][8][9][10][11][12][13][14][15][16][17][18] due to its potential application in curing heart disease and neuronal disease, etc. Within the study of spiral wave and spatiotemporal chaos, reaction-diffusion equations and arrays of oscillators are often used to simulate the formation and development of spiral wave and spatiotemporal chaos, and some critical bifurcation parameters are often changed to investigate the phase transition of patterns [19].…”

Section: Introductionmentioning

confidence: 99%

Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

Wang

Liu

et al. 2011

Nonlinear Dyn

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In this paper, a certain kind of intermittent scheme is used to control the chaos in a single chaotic Chua circuit to reach an arbitrary orbit. Furthermore, it is confirmed to be effective in suppressing spatiotemporal chaos and a spiral wave in the networks of Chua circuits with nearest-neighbor connections. The controllable and measurable variable is sampled, and the linear error between the sampled variable and the selected thresholds is fed back into the system only if the sampled variable exceeds the thresholds; otherwise, the system will develop itself without any external perturbation. In experiments, the control scheme could be realized by using the Heavside function. In the case of one single chaotic Chua circuit, the chaotic state can be controlled to reach an arbitrary n-periodical orbit (n = 1, 2, 3, 5, 6, . . .) with appropriate feedback intensity and thresholds. It is argued that this scheme could explain the mechanism of what is called phase compression. Then the phase compression scheme is used to control a spiral wave and spatiotemporal chaos in a network of Chua circuits with 256 × 256 sites. The numerical simulation results confirm its effectiveness when appropriate upper and bottom thresholds are used by monitoring the measurable output voltages of the chaotic circuit in one site of the network.

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Section: Introductionmentioning

confidence: 99%

Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

Wang

Liu

et al. 2011

Nonlinear Dyn

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“…In the space-time chaotic control of the one-dimensional CGL system, the system expansion does not affect the density of the controllers required for the realization of the control (Boccaletti and Bragard, 2006). The helical and multihelical waves in the CGL system are suppressed by local feedback control (Ma et al, 2008). The CGL equation is used to describe the dynamics of the oscillating medium, and the influence of the boundary on the frequency of spiral rotation is studied (Aguareles, 2014).…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control of complex Ginzburg–Landau system

Cai

Dai

Zhang

et al. 2022

Transactions of the Institute of Measurement and Control

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Different from the existing research on iterative learning control (ILC) real-valued systems, complex-valued partial differential system is studied in this paper. All variables and parameters of the system are complex, and distributed control is imposed on the system. First, the original complex system is transformed into two coupled real systems, which represent the real and imaginary parts of the original complex system, respectively. Second, a complex [Formula: see text]-type ILC algorithm is designed that the real and imaginary parts of the learning law are coupled to each other. Then, the contraction mapping principle and analytical techniques are used to ensure that the tracking error converges to zero in the sense of [Formula: see text]-norm. Finally, a numerical simulation is presented to show the effectiveness of the proposed algorithm.

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“…Motivated by some recent articles, that were investigated on spatiotemporal patterns away from the equilibriums, traveling waves [6], spiral waves which frequently occur in biological, chemical and other physical systems [11,13,28,29,41,42,46]. We introduce the solution of the general amplitude equations and prove its well-posedness (for Hopf bifurcation [10,12,26,27] and Turing instabilities [40,45]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Spatially Extended Excitable Izhikevich Neuron Model near Instability

Mondal

Sharma

et al. 2021

Preprint

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The article focuses on the issue of a spatiotemporal excitable biophysical model that describes the propagation of electrical potential called spikes to model the diffusion induced dynamics based on an analytical development of amplitude equations. Considering the Izhikevich neuron model consisting of coupled systems of ODEs , we demonstrate various results of spatiotemporal architecture ( PDEs ) using a suitable parameter regime. We analytically perform the saddle node bifurcation and Hopf bifurcation analysis with bifurcating periodic solutions that show the transition phases in the system dynamics. We study different types of firing patterns both analytically and numerically by the formation of Riccati differential equation. To examine the characteristics of diffusive instabilities, we use Turing amplitude equations by multiscaling method and then expansion in powers of a small control parameter. The instabilities and Turing bifurcation are established using the theoretical analysis and numerical simulations. The spatial system has potential effects on the deterministic system as a result of the diffusive matrices with various couplings and the coupled oscillators with this nearest neighbor coupling show synchronization measured by the synchronization factor analysis. Our results qualitatively reproduce different phenomena of the extended excitable system based with an efficient analytical scheme.

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Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation

Cited by 26 publications

References 16 publications

Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits

Iterative learning control of complex Ginzburg–Landau system

Analysis of Spatially Extended Excitable Izhikevich Neuron Model near Instability

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