Hindmarsh-Rose 神经网络的混沌同步

研究了通过特殊构造的非线性函数耦合连接的神经网络的混沌同步问题。在发展基于稳定性准则的混沌同步方法的基础上,给出了计算同步稳定性的误差发展方程,当耦合强度取参考值时,可实现稳定的混沌同步而不需要计算最大条件Lyapunov指数去判定是否稳定。通过对按照完全连接形式构成的Hindmarsh-Rose神经网络的数值模拟,显示可仅从两个耦合神经的耦合强度的稳定性范围预期到许多耦合神经实现同步的稳定性范围。该方法在噪声影响下,对实现神经元的混沌同步仍具有较强的鲁棒性。此外发现随着耦合神经数的增加,满足同步稳定性的耦合强度减小,与耦合神经的数量成反比。     

SIR传染病模型的混沌跟踪控制

研究了一类疾病传染率受季节因素影响的SIR传染病模型的混沌运动,并采用轨迹跟踪控制方法对传染病模型中的混沌运动进行控制,设计状态反馈控制器,控制系统输出跟踪某一理想状态,使染病者数量渐近趋于零,从而,达到消除疾病的目的．仿真结果表明该方法的有效性．     

可兴奋细胞CHAY模型的混沌控制

对可兴奋细胞的Ｃｈａｙ模型的混沌解进行控制。控制的方法为：（１）参数周期扰动;（２）周期激励;（３）周期脉冲（拍）激励。用这三种方法都实现了把混沌转化为周期运动。     

人心脏低维动力学模型的混沌控制

两个相互作用振子的非线性动力学行为由特定的一维双参量圆周映射概括。这一模型已经被成功地用于描述人心脏某些反常节律。本文将相加性开环加闭环（ＯＰＣＬ）控制机制引入人心脏低维动力学模型,设计了一种有效的、抗噪声干扰的控制技术,可以通过变更迫动项实现任意期望的周期轨道的稳定控制。计算机模拟实验证实：运用这种方法能够将相空间中任意的初始状态引导到预先规定的目标动力学状态。     

离散广义Logistic模型的混沌控制

利用Lyapunov指数方法,验证了一类离散广义Logistic模型存在混沌现象,并采用混沌控制中OGY方法的基本思想,研究了这类模型的混沌控制问题,得出了消除混沌,保持种群稳定到不动点和2-周期轨道的充分条件．     

具有共生作用两种群离散耦合Logistic模型混沌控制

针对具有共生作用的离散耦合Logistic模型,首先采用Lyapunov指数方法验证了混沌现象的存在.然后详细地分析了系统随参数变化的分岔图,发现了系统中存在更复杂的现象.最后应用混沌跟踪控制方法控制系统的混沌现象,使得种群稳定到正不动点轨道上,消除了种群中存在的混沌现象.仿真结果验证了控制方法的有效性.     

基于混沌降噪的神经元放电峰峰间期序列分析

围绕如何来消除神经元峰峰间期序列中随机噪声影响从而提取出决定不规则性的确定性动力学关系这个问题,本文首先简要介绍峰峰间期序列样本的制备,然后着重讨论一个简单可行的混沌时间序列降噪方法的原理和算法实现,最终将该方法运用到神经元放电活动数值模拟和实验记录到的峰峰间期时间序列样本分析中。本文分析结果再次证明神经放电活动中确实存在着不规则混沌运动,而且降噪结果进一步揭示了神经电生理实验中决定混沌放电的不连续但分段光滑的单峰函数关系     

一类离散捕食-食饵模型的混沌跟踪控制

针对一类离散捕食食饵系统,采用Lyapunov指数方法、绘制系统分岔图和混沌吸引子等方式验证了混沌现象的存在.为了消除系统的混沌现象,根据控制理论的轨迹跟踪控制原理,设计混沌跟踪控制器将系统控制到任意给定的期望周期轨道上,达到了稳定种群的目的.仿真分析表明了所设计控制器的有效性.     

生态模型中混沌与分形结构的屏幕造形

一、引言差分模型在理论生态研究中有重要意义。对于这种具有离散时间的半动态系统的传统研究,例如周期解,稳定性等(Lasalle,1976)有较为全面的系统研究。他发现Liapunov函数     

基于时滞反馈的一类基因表达模型的分岔控制

针对一类具时滞的基因表达模型的Hopf分岔控制问题,提出一种基于时滞反馈的分岔控制方法.以时滞为分岔参数,指出无控制的系统当时滞增加到一定数值时,稳定性遭到破坏,使Hopf分岔过早产生.引入时滞反馈控制器可以延迟有害Hopf分岔的发生或使Hopf分岔消失,最后通过数值模拟验证了该理论的正确性.     

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value.     

Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation

The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary neuronal model that reproduces the main characteristics of real neurons. In this paper, we introduce a QIF neuron with a nonlinear adaptive current. This model reproduces the neuron-computational features of real neurons and is analytically tractable. It is shown that under a constant current input chaotic firing is possible. In contrast to previous study the neuron is not sinusoidally forced. We show that the spike-triggered adaptation is a key parameter to understand how chaos is generated.     

一类非线性环链系统的混沌反控制

针对一类系统—非线性环链系统,利用非线性反馈控制的方法,研究了该系统的混沌反控制问题.该方法不需计算Lyapunov函数,从而降低了混沌反控制的计算量.仿真结果表明了该系统可快速有效地跟踪给定的混沌系统,充分的显示了该系统的优势.     

Signal integration on the dendrites of a pyramidal neuron model

This paper studied the synaptic and dendritic integration with different spatial distributions of synapses on the dendrites of a biophysically-detailed layer 5 pyramidal neuron model. It has been observed that temporally synchronous and spatially clustered synaptic inputs make dendrites perform a highly nonlinear integration. The effect of clustering degree of synaptic distribution on neuronal responsiveness is investigated by changing the number of top apical dendrites where active synapses are allocated. The neuron shows maximum responsiveness to synaptic inputs which have an intermediate clustering degree of spatial distribution, indicating complex interactions among dendrites with the existence of nonlinear synaptic and dendritic integrations.     

Chaotic dynamics of a three species prey-predator competition model with bionomic harvesting due to delayed environmental noise as external driving force

We consider a biological economic model based on prey-predator interactions to study the dynamical behaviour of a fishery resource system consisting of one prey and two predators surviving on the same prey. The mathematical model is a set of first order non-linear differential equations in three variables with the population densities of one prey and the two predators. All the possible equilibrium points of the model are identified, where the local and global stabilities are investigated. Biological and bionomical equilibriums of the system are also derived. We have analysed the population intensities of fluctuations i.e., variances around the positive equilibrium due to noise with incorporation of a constant delay leading to chaos, and lastly have investigated the stability and chaotic phenomena with a computer simulation.     

Motor neuron degeneration in a mouse model of seipinopathy

Heterozygosity for missense mutations (N88S/S90L) in BSCL2 (Berardinelli–Seip congenital lipodystrophy type 2)/Seipin is associated with a broad spectrum of motoneuron diseases. To understand the underlying mechanisms how the mutations lead to motor neuropathy, we generated transgenic mice with neuron-specific expression of wild-type (tgWT) or N88S/S90L mutant (tgMT) human Seipin. Transgenes led to the broad expression of WT or mutant Seipin in the brain and spinal cord. TgMT, but not tgWT, mice exhibited late-onset altered locomotor activities and gait abnormalities that recapitulate symptoms of seipinopathy patients. We found loss of alpha motor neurons in tgMT spinal cord. Mild endoreticular stress was present in both tgMT and tgWT neurons; however, only tgMT mice exhibited protein aggregates and disrupted Golgi apparatus. Furthermore, autophagosomes were significantly increased, along with elevated light chain 3 (LC3)-II level in tgMT spinal cord, consistent with the activation of autophagy pathway in response to mutant Seipin expression and protein aggregation. These results suggest that induction of autophagy pathway is involved in the cellular response to mutant Seipin in seipinopathy and that motoneuron loss is a key pathogenic process underlying the development of locomotor abnormalities.     

A model predictive control based scheduling method for HIV therapy

Recently developed models of the interaction of the human immune system and the human immunodeficiency virus (HIV) suggest the possibility of using interruptions of highly active anti-retroviral therapy (HAART) to simulate a therapeutic vaccine and induce cytotoxic lymphocyte (CTL) mediated control of HIV infection. We have developed a model predictive control (MPC) based method for determining optimal treatment interruption schedules for this purpose. This method provides a clinically implementable framework for calculating interruption schedules that are robust to errors due to measurement and patient variations. In this paper, we discuss the medical motivation for this work, introduce the MPC-based method, show simulation results, and discuss future work necessary to implement the method.     

The role of a transient potassium current in a bursting neuron model

Presented here is a biophysical cell model which can exhibit low-frequency repetitive activity and bursting behavior. The model is developed from previous models (Av-Ron et al. 1991, 1993) for excitability, oscillations and bursting. A stepwise development of the present model shows the contribution of a transient potassium current (I _A ) to the overall dynamics. By changing a limited set of model parameters one can describe different firing patterns; oscillations with frequencies ranging from 2–200 Hz and a wide range of bursting behaviors in terms of the durations of bursting and quiescence, peak firing frequency and rate of change of the firing frequency.