The investigation of the some chaotic systems by mathematical physi̇cs

In this work the investigations of physical and social complex networks have been taken into account. The development of complex networks take place through a fractal space with a non-Markovian manner . The interaction of the elements that compose the real networks plays an important role in their behaviour . In this respect, standard distributions are inadequate to handle the complex networks. In complex networks, it is observed that the power-law distributions become prominent instead of the exponential distributions. In this study, random Erdös-Renyi model, Barabasi-Albert model which is a scale-free network, deterministic scale-free networks and Kuramoto model are introduced. The phase transition of the collective behaviours of the particles that compose the system in condensed matter in a spesific critical temperature is analagous to the change in topological behaviours that is encountered in a spesific critical value of the number of the links within the networks. Based on this analogy, it is possible to analyze the second-order phase transitions in parallel with the topological behaviours of the networks. And finally we arrived to the conclusion that by the determination of basic principals on which the network systems are based on, the modelling, the prediction of the behaviour and the controlling the network systems become possible.