Decision-making Behavior And Chaos Synchronization Of Biological Complex Networks

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-MakingWhen 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-MakingThe 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 behaviorsThe 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 networksOn 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.