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目的研究单个Hindmarsh-Rose(H-R)神经元模型从周期动力学模式转向混沌模式的自适应反控制问题。方法利用施加正弦函数延迟自反馈方法进行数值模拟分析,分别将耦合强度和时间延迟作为控制参数。结果通过大量的数值模拟计算,给出神经元的膜电位变量随耦合强度和时间延迟两个参数变化的分岔图,发现在耦合强度值和时间延迟两个参数组合的一些范围内,本来是3峰周期动力学模式的H-R神经元运动可被反控制成混沌模式及其他周期模式的运动。结论对H-R神经进行反控制的正弦延迟自适应反馈法是有效的,耦合强度和时间延迟均为反控制的重要参数。控制过程反映了神经独有的自适应的信息识别的动力学特性。
Aim To study the adaptive inverse control of a single Hindmarsh-Rose (H-R) neuron model from periodic dynamical model to chaotic model. The method uses the sine function delay self-feedback method to carry on the numerical simulation analysis, and takes the coupling strength and the time delay as the control parameters respectively. Results A large number of numerical simulations were performed to show the bifurcation diagrams of the changes of the neurons’ membrane potential variables with the coupling strength and the time delay. It was found that in some ranges of the combination of the two values of the coupling strength and the time delay, HRP motions in 3-peak-cycle kinetics can be back-controlled into chaotic and other periodic modes of motion. Conclusion The sinusoidal delayed adaptive feedback method for the anti-control of H-R nerve is effective. Both the coupling strength and the time delay are important parameters of anti-control. The control process reflects the dynamics of neural-only adaptive information recognition.