Tam ve küme eşzamanlılığı gösteren kaotik dinamik ağların ortalama toplamsal nedensellik entropisi ile analizi

The chaotic dynamical systems with characteristically irregular and unpredictable behavior can form synchronized complex networks when allowed to interact. The main aim of this thesis is to analyze the synchronized chaotic networks in the view of information theory and to discover the network connectivity information using the information-theoretic measures. The entropy-based measures estimated from observations are a valuable way to quantify information flow between the subsystems since they can provide a model-free approach for identifying network structures. This thesis initially addresses estimating the entropy-based measures to represent the information flow accurately. A comparative study has been conducted with the existing measures and the estimators. A new k-nearest neighbor causation entropy estimator based on the existing causation entropy measure and other similar estimators has been proposed to represent information flow effectively. This thesis mainly focuses on inferring the unknown network properties using limited observations in directed chaotic synchronized networks even if the underlying dynamics and connections of the network are unknown. The problem is compelling since the observations in synchronized systems are identical. On the other hand, the systems can temporarily be perturbed to destroy synchronization. The average integrated causation entropy measure, proposed herein, evaluated in the partially reconstructed state space of the network, can be used to determine network connectivity as the systems tend to resynchronize after perturbations. The average integrated causation entropy properties have been investigated analytically, and a novel algorithm has been developed to reveal the network coupling matrix. It has been found that the proposed measure and related algorithm based on the difference of average integrated causation entropy reveals the network structure in random networks in complete synchronization. We have also shown that the proposed measure can be used to detect clusters in chaotic cluster synchronization networks. A novel algorithm has been suggested based on the k-means clustering of the proposed measure with only single series of observation. The results indicate that the proposed procedure can distinguish the systems regarding their memberships in the clusters formed.