Eliminating chaos in the Belousov–Zhabotinsky reaction by no-delay feedback and delayed feedback
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We present numerical simulations of the three-variable model of the Belousov–Zhabotinsky reaction developed by Gyorgyi and Field, where chaos can occur in the free-running system. As the rate of in-flow in the continuous-flow stirred-tank reactor is controlled by the concentration of one of the reactor species through a feedback loop, we find two simple ways to bring the chaotic behavior to periodic behavior. One is to modify the feedback strength without time delay in the feedback loop, and the other is to modify the delay time of the feedback at constant feedback strength. The possible mechanisms for the two ways are discussed.
KeywordsNonlinear chemistry dynamics Chaos control Feedback Delay time
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The authors gratefully thank Shawn T. Brown for valuable comments. This work is supported by the National Natural Science Foundation of China.