摘要
生物复杂网络近年来受到了科学与工程各个领域研究者越来越多的关注,成为近年来研究的一个热点。通过对生物复杂网络动力学性质的研究,一方面可以使我们更好地了解和解释生物世界中复杂网络所呈现出来的各种动力学现象,如稳定、同步、抉择等;另一方面我们可以将对复杂网络动力学性质研究的理论成果应用到具体问题中去,如可以设计出具有更好特性的实际网络或使网络处于对我们有利的状态,使得网络理论可以为我们所用。另外,复杂网络领域的研究表明网络结构能显著地影响它的动态行为,过去对生物网络的建模用的都是规则网络或随机网络,而事实上生物网络的拓扑不可能是完全规则或完全随机的,应介于两者之间。因此,对生物复杂网络拓扑性质研究的重要意义是显而易见的。
本论文将统计方法、非线性系统理论、控制理论以及矩阵理论等理论和方法应用到生物复杂网络的研究中,创新性地将复杂网络(complex network)和生物抉择(Decision-Making)联系起来,对生物复杂网络的抉择行为和混沌同步两个方面的动力学行为进行了研究。本文的主要内容和创新之处可概述如下:
1.生物抉择行为的网络建模研究
由于当前对生物网络的研究中,网络模型都以单纯的随机或规则网络来建立的,而事实上很多生物网络都是介于这两者之间的。复杂网络的研究成果表明,许多网络都具有小世界或无标度的特性。本文以生物抉择网络为研究对象,探讨生物抉择行为的网络建模,构建了一个递归网络模型来仿真大脑的抉择过程,并且分别建立了规则网络,随机网络和小世界网络和无标度网络四种不同拓扑结构的网络模型,并对其网络特性做了研究分析。这对于生物网络模型的建立拓开了思路,使得生物网络模型的研究更符合实际,得到的研究成果将推动生物复杂网络领域的研究进展。
2.网络拓扑对生物抉择行为的影响研究
当网络拓扑变化时,生物抉择行为会受到哪些影响?在规则网络、小世界、无标度和随机网络四种不同的拓扑结构下,网络行为会受到哪些影响?复杂网络领域的研究表明网络结构能显著地影响它的动态行为(见[3]Albert & Barabasi,2002;[4]Newman,2003;[5]Boccaletti et al.,2006)。然而,到目前为止,还没有理论方面的工作用来揭示网络结构对抉择行为的潜在影响。在上述模型的基础上,本文研究分析了四种不同拓扑类型的网络,即规则网络、小世界网络、无标度网络和随机网络对生物抉择行为的影响。通过实验分析发现,规则网络和小世界网络在四种网络中显示出明显更高的准确选择率。无标度网络显示出中等的准确选择率,而随机网络显示出最差的性能。以反应时间而论,小世界网络显示了最好的性能,而随机网络仍旧显得最差。规则网络和无标度网络显示了中等的反应时间。同时考虑准确选择率和反应时间,小世界网络显示出最好的抉择性能。
3.内部噪声对网络抉择行为的影响研究
由于受到神经元内部或者外部环境的影响,生物抉择过程可能不完全是可控的。这些自发活动可以是大脑中的随机背景输入激活,而不是来自外部刺激。为了揭示内部噪声对抉择过程的影响,本文引入了内部噪声米模拟神经自发活动。通过实验分析比较,得出随机网络有最好的能力在一个较宽的范围内抑制内部噪声,而无标度网络显示出最差的抗噪声能力。规则网络和小世界网络有类似中等的抑制噪声能力。
进一步,为分析内部噪声对抉择过程的影响,本文比较了在外部刺激和高内部噪声情况下的网络行为。在高内部噪声时,随机网络显示了最好的准确选择性能。而在低噪声时,显示了最差的性能。这个戏剧性的网络行为变化进一步证明了随机网络具有较好的抗噪声能力。其它三种网络显示了类似的准确选择性能。然而,在反应时间方面,随机网络仍旧显示出最差。另外,在所有网络中,无标度网络显示了最快的反应时间。
4.神经损伤对网络抉择行为的影响研究
神经系统可能会被一些物理的或者生物的过程损伤,譬如机械性的神经伤害或神经退行性疾病。本文模拟了这些神经伤害来考察抉择在不同拓扑结构网络下的网络行为,分别考察了两种不同模式的网络损伤(成簇损伤和分布式损伤模式)下各种网络拓扑的网络抉择行为。经过实验分析发现,在神经损伤的情况下,特别是大范围分布式神经损伤,小世界网络保持着最好的能力来执行抉择过程,显示出小世界网络在选择性的抉择过程中表现出相对稳定的网络行为。
在此基础上,我们对造成上述网络行为变化的原因进行了分析探讨,指出了网络行为的改变和拓扑性能的变化有着很强的相关性,一些脑结构的形成(譬如脑干的网状体)是小世界网络而不是无标度网络,不同的损伤模式对网络行为可能会有不同的影响。
5.小型生物网络混沌同步动力学研究
本文在对现有混沌同步方法研究的基础上,对小型生物网络的混沌同步提出了一种具有一般意义的同步方法,将非线性的同步问题转化为线性时变系统来解决,分析了系统的稳定性能,并得出了一些有价值的结论。为小型生物网络系统混沌同步的研究提供了新的思路。
我们调查了皮层神经网络中一类具有未知参数的小型生物网络混沌系统,通过合理的假设,该类非线性混沌系统可以作为线性的时变系统来处理,同步问题可以通过最优滤波的方法解决,这时卡尔曼滤波的结论可以被采用。即使不通过线性化,线性技巧在我们提出的方法中也是可用的。我们也给山了一些充分条件,在此情况下,响应系统的状态能够渐近跟踪驱动系统的状态,并且在可观测输出端包含干扰噪声的情况下,仍能保证好的跟踪轨迹。这一结果,为具有兴奋性和抑制性耦合的神经振子群中神经元集群的同步控制研究起到了指导作用。
Recently,biological complex networks attract more and more attentions from various fields of science and engineer.By studying the dynamic behaviors of biological complex network,on one hand,we can understand and explain the dynamic behaviors in real-world networks,such as stability,synchronization,decision-making; and on the other hand,we can apply these theoretical results to some practical applications,for example,we can apply these results to the design of real networks to achieve good performance or to control of real networks to achieve some desirable network behaviors that benefit the networks.In addition,the research of biological complex networks shows network structures can strongly affect their dynamic behaviors.Usually we use the regular or random networks to construct biological network models.In fact,biological networks are not completely regular or random systems,which should contain both components.So,the importance of studying topologies and properties of biological complex networks is clearly self-evident.
In this dissertation,we apply statistical method,nonlinear system theory,control theory and matrix theory to the research of biological complex networks,and we study the decision-making behavior of biological complex networks,as well as the chaos synchronization in a small biological network system through originalily corelating the study of complex network with Decision-Making.The main contents and originalities in this paper can be summarized as follows:
1.Modeling of decision-making behavior in biological complex networks
Recently,a large volume of models concerning on biological networks focus on the pure random or regular networks.However,the topology of a biological network often lies between being completely regular and being completely random.The study on complex networks has rewaled that many networks display small-world or scalefree properties.In this dissertation,we study the network model to simulate biological decision-making.We generated a recurrent network model with four structures, namely,regular,random,the small-world and the scale-free networks,and then we analyzed topological properties of these networks.Our study contributes to the advance of modeling of biological networks.
2.Impact of Network Topology on Decision-Making
When network topology changes,does biological decision-making behavior change? Or do different topological networks show different network behaviors? The study on complex networks has revealed that the architecture of a network can significantly influences its dynamical behaviors(for reviews,see[3]Albert & Barabasi,2002;[4]Newman,2003;[5]Boccaletti et al.,2006).So far,however,no theoretical work has explored the potential impact of network topology on decisionmaking. Based on the network model mentioned above,we study the effects of network topology on biological decision-making.We found that the regular and the small-world networks show the highest accuracy among the four networks in a wide range of coherence levels.The scale-free network shows medium accuracy,while the random network displays the worst performance.With respect to reaction time,the small-world network shows the best performance,while the random network still shows the worst performance.The regular and the scale-free networks display medium reaction time.Considering both accuracy and reaction time,the small-world network offers the best performance in decision-making.
3.Effects of internal noise on Decision-Making
The biological decision-making process might not be entirely reliable due to the noise in the sensory system or in the environment.These neuronal spontaneous activities may be activated by stochastic background inputs inside the brain,rather than external stimuli.To study the effects of internal noise on decision-making,we introduced the internal noise to mimic neuronal spontaneous activities.Analysis of network behaviors shows that the random network has the best capacity to resist the internal noise in a wide range,while the scale-free network shows the worst performance of noise-resistant capacity.The regular and the small-world networks have the similar medium noise-resisting capacity.
To further investigate the effects of the internal noise on the decision-making process,we compared the network behaviors in the presence of both external stimuli and high internal noise.We found that the random network shows the best performance of correct choice in the high noise instead of the worst performance in the low noise.This dramatic change in network behavior further confirms the good noise-resisting capacity of the random network.The other three networks show similar performance of correct choice.However,the random network still shows the worst performance in terms of reaction time.In addition,the scale-free network shows the shortest reaction time among all networks.
4.Effects of neuronal damages on network behaviors
The nervous system may be damaged by some physical or biological processes, such as mechanical neural injury or neurodegenerative disease.Here we mimicked these neuronal damages to examine network tolerance during the decision-making process in different topological networks.We introduced two kinds of damage patterns:the clustered and the distributed damage patterns.In the case of neuronal damages,especially largely distributed neuronal damages,the small-world network retains the best capacity to execute the decision-making process.All these results indicate that the small-world network exhibits relatively stable network behaviors in decision-making.
Then,we investigated the mechanism underlying the changes in network behaviors.Our results indicate strong correlations between the changes in network behaviors and the changes in topological features.T he formation of some brain structure,such as the brainstem reticular formation,is a small-world,but not scalefree, network.Our results also indicate that different damage patterns may have different effects on decision-making.
5.Study of chaos synchronization on small biological networks
On basic of the research of chaotic synchronization methods,a general synchronization method is proposed for a class of small biological network chaotic systems.We resolved the synchronization problem by treating the nonlinear system as the linear time-varying system,and analyzed the stability properties,got some valuable conclusions.Our study proposed a new idea for the research of chaotic synchronization.
We investigated a class of small biological complex network chaotic systems with uncertain parameters in cortex.Under some mild conditions,it is shown that the class of nonlinear chaotic systems can be treated as linear time-varying systems,driven by the additive white noise contaminated at the receiver,or the observed output.The synchronization is tackled via optimal filtering to which the results of Kaiman filtering can be applied.We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asympto cally,and good tracking performance can be obtained in the presence of the additive white noise involved in the observed output.These results can promote the synchronization research of neuronal population with excitatory and inhibitory connections.
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