Control Chaos in Hindmarsh--Rose Neuron by Using Intermittent Feedback with One Variable

The mechanism of the famous phase compression is discussed, and it is used to control the chaos in the Hindmarsh--Rose (H-R) model. It is numerically confirmed that the phase compression scheme can be understood as one kind of intermittent feedback scheme, which requires appropriate thresholds and feedback coefficient, and the intermittent feedback can be realized with the Heaviside function. In the case of control chaos, the output variable (usually the voltage or the membrane potential of the neuron) is sampled and compared with the external standard signal of the electric electrode. The error between the sampled variable and the external standard signal of the electrode is input into the system only when the sampled variable surpasses the selected thresholds. The numerical simulation results confirm that the chaotic H-R system can be controlled to reach arbitrary n-periodical (n=1, 2, 3, 4, 5, 6, ...) orbit or stable state even when just one variable is feed backed into the system intermittently. The chaotic Chua circuit is also investigated to check its model independence and effectiveness of the schemes and the equivalence of the two schemes are confirmed again.