神经元混沌、同步与控制
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摘要
神经元在中枢神经系统信息处理过程中起着关键的作用,神经元信息的产生和传输体现了丰富的非线性特征。因此,单神经元与耦合多神经元的非线性动力学研究具有重要意义。研究发现,神经元在外部刺激下会产生不同的放电模式,如拟周期、混沌放电以及神经元同步放电现象。
本文首先建立了外电场作用下柱状细胞的电缆模型。在模型中,引入了Fitzhugh-Nagumo(FHN)模型的恢复变量来描述动作电位的慢变过程;然后,详细分析了不同频率外部电场作用下神经元的非线性动力学规律。通过数值分析发现了包括极限环、拟周期振荡和混沌在内的复杂的非线性行为,应用Lyapunov指数、功率谱以及相平面等方法证明了混沌存在。
细胞间的信号同步行为在神经系统信号传输中扮演了非常重要的角色,间隙耦合的神经元同步问题是本文主要研究内容之一。本文基于单神经元模型,首次提出了间隙耦合的两个和多个神经元的模型,分析了细胞间隙耦合强度对神经元同步的影响,给出了神经元之间达到同步的充分条件。
时滞是影响神经元之间信号传递的一个主要因素,本文研究了时滞耦合神经元之间的同步问题。建立了时滞耦合的多神经元模型,分析了神经元之间的时滞时间和耦合强度对神经元同步的影响,得到了与时滞大小和耦合强度均有关的耦合神经元同步的条件。
神经元的混沌是某些神经系统疾病与疾病改善的体现。外部刺激可以改变神经元的同步特性。本文首次提出了Lyapunov控制、Backstepping控制和变论域自适应模糊控制来实现神经元的同步。由于神经元的参数和外部条件的非线性特性,本文采用模糊逼近和H_∞控制保证系统的鲁棒性。
通过数值仿真,证明了上述理论的正确性和控制算法的有效性。
以上研究内容为脑科学、针灸的量化分析以及一些神经系统疾病的治疗提供了理论支持。
The neurons are believed to be the key elements in the signal processing of neural system.The generation and transmitting of neural information are nonlinear, so the dynamic performances of individual or coupled neurons get the main focus in the neuroscience research. It was found that the neurons can fire in different patterns, such as chaos and quasi-period, and coupled neurons can fire synchrously under external stimulation.
Firstly in this dissertation, the cable model of a cylindrical cell in external electrical stimulation is established and the recovery variable based on the Fitzhugh-Nagumo (FHN) model is introduced to describe the slow process of firing. Then, the dynamic performances of single neuron under external electrical stimulation with varied frequency have been analyzed in detail. The complex nonlinear phenomenons such as limit cycle, quasi-period oscillation and chaos were found in the simulation, and the chaos of active potential is demonstrated by Lyapunov exponent, power spectra and phase plane.
The synchronization of coupled neurons plays the main role in the process of neural informations tansmiting, so the research on the synchronization of neurons coupled with gap junction is one of the main contents of this dissertation. The model of two or more neurons coupled with gap junction is established on the base of single neuron model to study the influence of the coupling strength of gap junction on the synchronization and the sufficient condition of synchronization is given.
Time delay is the main fator to affect the informations transmitting among neurons, so this dissertation is also dedicated to study the synchronization of time-delay coupled neurons. The model of time-delay coupled neurons has been established to study the effects of time delay and the coupling strength on the synchronization and the sufficient condition of delay coupled neurons synchronization which relates to the time delay and coupling strength is given.
The chaotic synchronization in neurons may imply some neural diseases or the improvement of these diseases. As the external stimulation can change the sysnchronization in neurons, in this dissertation, the Lyapunov control, Backstepping control and variable universe adaptive fuzzy control have been applied to synchronize the neurons. The parameters of neuron model and the external condition of neuron are nonlinear, so the fuzzy approximation and H_∞control are employed to guarantee the robustness of the system.
The results of simulation demonstrated the validity of the theoretic analysis and control algorithms refered to above.
The conclusions of this dissertation can benefit the researches on the brain, the quantitative analyze of acupuncture and the treatment of some neural disease.
本文首先建立了外电场作用下柱状细胞的电缆模型。在模型中,引入了Fitzhugh-Nagumo(FHN)模型的恢复变量来描述动作电位的慢变过程;然后,详细分析了不同频率外部电场作用下神经元的非线性动力学规律。通过数值分析发现了包括极限环、拟周期振荡和混沌在内的复杂的非线性行为,应用Lyapunov指数、功率谱以及相平面等方法证明了混沌存在。
细胞间的信号同步行为在神经系统信号传输中扮演了非常重要的角色,间隙耦合的神经元同步问题是本文主要研究内容之一。本文基于单神经元模型,首次提出了间隙耦合的两个和多个神经元的模型,分析了细胞间隙耦合强度对神经元同步的影响,给出了神经元之间达到同步的充分条件。
时滞是影响神经元之间信号传递的一个主要因素,本文研究了时滞耦合神经元之间的同步问题。建立了时滞耦合的多神经元模型,分析了神经元之间的时滞时间和耦合强度对神经元同步的影响,得到了与时滞大小和耦合强度均有关的耦合神经元同步的条件。
神经元的混沌是某些神经系统疾病与疾病改善的体现。外部刺激可以改变神经元的同步特性。本文首次提出了Lyapunov控制、Backstepping控制和变论域自适应模糊控制来实现神经元的同步。由于神经元的参数和外部条件的非线性特性,本文采用模糊逼近和H_∞控制保证系统的鲁棒性。
通过数值仿真,证明了上述理论的正确性和控制算法的有效性。
以上研究内容为脑科学、针灸的量化分析以及一些神经系统疾病的治疗提供了理论支持。
The neurons are believed to be the key elements in the signal processing of neural system.The generation and transmitting of neural information are nonlinear, so the dynamic performances of individual or coupled neurons get the main focus in the neuroscience research. It was found that the neurons can fire in different patterns, such as chaos and quasi-period, and coupled neurons can fire synchrously under external stimulation.
Firstly in this dissertation, the cable model of a cylindrical cell in external electrical stimulation is established and the recovery variable based on the Fitzhugh-Nagumo (FHN) model is introduced to describe the slow process of firing. Then, the dynamic performances of single neuron under external electrical stimulation with varied frequency have been analyzed in detail. The complex nonlinear phenomenons such as limit cycle, quasi-period oscillation and chaos were found in the simulation, and the chaos of active potential is demonstrated by Lyapunov exponent, power spectra and phase plane.
The synchronization of coupled neurons plays the main role in the process of neural informations tansmiting, so the research on the synchronization of neurons coupled with gap junction is one of the main contents of this dissertation. The model of two or more neurons coupled with gap junction is established on the base of single neuron model to study the influence of the coupling strength of gap junction on the synchronization and the sufficient condition of synchronization is given.
Time delay is the main fator to affect the informations transmitting among neurons, so this dissertation is also dedicated to study the synchronization of time-delay coupled neurons. The model of time-delay coupled neurons has been established to study the effects of time delay and the coupling strength on the synchronization and the sufficient condition of delay coupled neurons synchronization which relates to the time delay and coupling strength is given.
The chaotic synchronization in neurons may imply some neural diseases or the improvement of these diseases. As the external stimulation can change the sysnchronization in neurons, in this dissertation, the Lyapunov control, Backstepping control and variable universe adaptive fuzzy control have been applied to synchronize the neurons. The parameters of neuron model and the external condition of neuron are nonlinear, so the fuzzy approximation and H_∞control are employed to guarantee the robustness of the system.
The results of simulation demonstrated the validity of the theoretic analysis and control algorithms refered to above.
The conclusions of this dissertation can benefit the researches on the brain, the quantitative analyze of acupuncture and the treatment of some neural disease.
引文
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