Abstract
Control of the spatiotemporal pattern with time delayed feedback in a gas discharge system is studied both analytically and numerically. The time delay in the semiphenomenological model is reduced as a perturbation. Based on the linear stability analysis, the effects of the time delay on the Turing and the Hopf modes near the Turing-Hopf codimension-two phase space are investigated. Then, the relations between the parameters of feedback and the oscillatory frequency, and the critical wavelength of the system are obtained. Results show that the transition between patterns can be controlled effectively by applying appropriate feedback even when the applied voltage keeps constant. The consequence of increasing the feedback intensity or the delayed time is equivalent to increasing the applied voltage. Furthermore, the analytical results are verified by two-dimensional numerical simulation. Our work proposes a way to control the pattern formation in a gas discharge system.
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