Intermittent Control Of Chaotic Systems And Complex Dynamical Networks As Well As Modeling And Analysis Of Biological Networks

This thesis is devoted to study some related work on complex systems.Firstly, a brief description of relevant research contexts is given, including thesynchronization and control of chaotic systems and complex dynamical net-works, as well as biological networks and microRNA. Secondly, the researchwork of the thesis is introduced, which focuses mainly on the following fouraspects:(1) Synchronization of delayed chaotic systems and delayed dynamical net-works via intermittent controlFirstly, we study the synchronization of coupled chaotic systems with time-varying delays in the presence of parameter mismatches by means of periodicallyintermittent control. Some novel and useful quasi-synchronization criteria areobtained by using the methods which are diferent from the techniques employedin the existing works, and the derived results are less conservative. Especially,a strong constraint on the control width that the control width should be largerthan the time delay imposed by the current references is released here. Moreover,our results show that the synchronization criteria depend on the ratio of controlwidth to control period, but not the control width or the control period. Secondly,we consider the problem of pinning synchronization for a class of complex de-layed dynamical networks via periodically intermittent control. Some novel andless conservative exponential synchronization criteria are obtained by utilizingmathematical induction method and the analysis technique. Moreover, a pinningscheme deciding what nodes should be chosen as pinned candidates and howmany nodes are needed to be pinned for a fixed coupling strength is provided.Simulation examples are finally given to illustrate the efectiveness of the theo-retical results.(2) Modeling of protein-protein interaction networks and emergence of itstopological propertiesScale-free connectivity, small-world pattern, hierarchical modularity and disassortativity are prominent features shared by most biological networks. Upto now, various network growth models invoking gene duplication and diver-gence have been proposed to understand the evolutionary mechanisms shapingthe scale-free connectivity, small-world pattern and disassortativity. Here, wepresent a simple evolution model of protein-protein interaction networks by in-troducing a rule of small-preference duplication of a node, meaning that the prob-ability of a node chosen to duplicate is inversely proportional to its degree, andsubsequent symmetric divergence plus nonuniform heterodimerization based onsome plausible mechanisms in biology. It is shown that our model cannot onlyreproduce sparseness, scale-free connectivity and small-world pattern, but alsoexhibit hierarchical modularity and disassortativity. After comparing the featuresof our model with those of real protein-protein interaction networks, we believethat our model can provide relevant insights into the mechanism underlying theevolution of protein-protein interaction networks.(3) Mean field theory for biology inspired duplication-divergence networkmodelWe derive mean-field analytic results and conduct simulation verificationfor a model describing the growth and evolution of protein-protein interactionnetworks based on duplication, divergence, heterodimerization, and mutation.Specifically, we derive power-law exponents, βKfor average degree, γPfor de-gree distribution, γCfor clustering coefcient, and γnnfor degree correlation,as functions of parameters of the model: the deletion probability pd, the het-erodimerization probability ph, and the addition probability pc. All four expo-nents depend on the all important parameter pd, only when it is larger than thecritical value1/2will networks have the biological properties of sparseness andsmall-worldness. Otherwise γCdepends on phand none depends on pc. Thedegree distribution is scale free only in the large network size limit. For finitenetwork size, it has an exponential dependence on the degree, a dependencethat weakens (as a power-law) with increasing network size. Power-law expo-nents extracted from our large-scale simulations agree extremely well with the mean-field results. Our results may be used to gain insights on the behavior ofbiological networks, including its origin and development.(4) Dynamic modeling and analysis of microRNA-mediated double nega-tive feedback loopMicroRNAs (miRNAs) are a class of about22-nucleotide non-coding RNAs,which regulate gene expression post-transcriptionally through canonical basepairing to its target mRNAs, ultimately leading to a reduction in the levels of pro-tein encoded by the target mRNAs. Recently, computational and experimentalstudies have identified an abundance of motifs involving miRNAs and transcrip-tional factors (TFs). The simplest motif is a two-node miRNA-mediated doublefeedback loop (MDNFL) in which a TF suppresses an miRNA and the TF itselfis negatively regulated by the miRNA. Here, we present a general computationalmodel for the MDNFL based on biochemical regulations and explore its dynam-ics by using bifurcation analysis. Our results show that the MDNFL can behaveas a bistable switch for a wide range of kinetic parameters. These functionalfeatures are consistent with the widespread appearance of miRNAs in fate de-cisions such as proliferation, diferentiation, and apoptosis during development.It is hoped that the results presented here will provide a new view on how geneexpression is regulated by miRNAs and further guidance for experiments. More-over, the insight gained from this study is also expected to provide a basis for theinvestigation of more complex networks assembled by simple building blocks.