Anti-control of periodic firing in HR model in the aspects of position, amplitude and frequency.

This paper proposes a novel controller to control position, amplitude and frequency of periodic firing activity in Hindmarsh-Rose model based on Hopf bifurcation theory which is composed of linear control gain and nonlinear control gain. First, we select the activation of the fast ion channel as control parameter. Based on explicit criterion of Hopf bifurcation, a series of conditions are obtained to derive the linear gains of controller responsible for control of the location where the periodic firing activity occurs. Then, based on the control parameter, a series of conditions are obtained to derive the nonlinear gains of controller responsible for controlling the amplitude and frequency of periodic firing activity by using center manifold and normal form. Finally, the numerical experiments show that our controller can make the periodic firing activity occur at designed value and control the amplitude and frequency of periodic firing activity by adjusting nonlinear control gain of controller.

Anti-control of sine function-delay feedback for H-R neuron / 医用生物力学

Objective To study the self-adaptive anti-control of a single H-R neuronal system transformed from periodic dynamics pattern to chaos. Methods Numerical analysis was performed by adding sine function self-delay feedback while coupling intensity and time-delay, respectively, as the control parameters. Results By numerical simulation and analysis, it was found that in a certain range of the combination of coupling intensity and time-delay, the time-interval sequences of the dynamical pattern of a single H-R neuronal system could be controlled from a periodical pattern of 3 spikes onto chaos and other periodical patterns. Conclusions The method of self-adaptive feedback of sine function is effective for the anti-control of H-R neuron, and the coupling intensity and time-delay are both important parameters. The particular self-adaptive dynamics of information identification to neuron is reflected in the control process.

Chaotic anti-control for the bounded linear continuous-time system / 西安交通大学学报·英文版

With regard to the bounded linear continuous-time system, a universal chaotic anti-controlling method was presented on the basis of tracking control. A tracking controller is designed to such an extent that it can track any chaotic reference input, thus making it possible to chaotify the linear system. The controller is identical in structure for different controlled linear systems. Computer simulations proved the effectiveness of the proposed method.

Chaotic anti-control for the bounded linear continuous-time system / 药物分析学报

With regard to the bounded linear continuous-time system, a universal chaotic anti-controlling method was presented on the basis of tracking control. A tracking controller is designed to such an extent that it can track any chaotic reference input, thus making it possible to chaotify the linear system. The controller is identical in structure for different controlled linear systems. Computer simulations proved the effectiveness of the proposed method.