The Study Of The Effect Of Topology Structures On Synchronization Transition In Coupled HR Neuron Cells System

In Recent years, the research on complex neuronal networks hasbeen attracting a lot of attentions. Internal cooperative behavior betweenneurons has a huge impact on biological systems network. Research onSynchronization and nonlinear characteristics of two electrically coupledHR neurons explained that the change of behavior of biological systemswas controlled by synchronizing transition between neurons; Studies onthe synchronization of HR neurons in two dimensional square latticeillustrates the coupling type of cells have a very significant impact in theregulation of the firing patterns; Research on small-world system firingpattern problems fully proved that electrical activity of neuronal cell has ahigh nonlinear characteristic and is very involute. These all promote thedevelopment of neuronal complex network system research. Until now,from different angles, many mathematical models of neurons hasestablished, such as FHN, HH, HR, ML, etc. This indicated that the studyof the complex neural networks has became a focus point.The evolutionary algorithm is gradually acting an increasinglysignificant role in the research in complex cell networks. Theevolutionary algorithm is not bound of restrictive assumptions insearching space, and make an assessment to guide the search process byusing the fitness function, so it has an extensive range of application. The evolutionary algorithms are developing step by step, such as the BPalgorithm combined with evolutionary algorithms make the computingspeed greatly increased; The evolutionary algorithm combined with thelocal optimization algorithm with rapid convergence avoid a lot ofrepetitive calculations.In this work, we started with four and five neuronal cell system andcarried out numerical calculation and analysis by using HR neuron cellkinetic model, then extended to more neurons composed of largersystems. And by using the evolutionary algorithms and averagesynchronization error, we studied the effects of the topology of neurons tothe synchronize transition.In the first chapter of this paper, we mainly introduced some basicknowledge, including nonlinear dynamics oscillating system, bifurcation,strange attractors and chaos, structure and function of neurons and theirkinetic model, the complex network configurations and topologies,evolutionary algorithms.In charter2, we introduced some theoretical knowledge. Such as thecharacteristics of the firing patterns under certain coupling topology, thesynchronization transition appeared in the non-coupling conditions in theexternal stimuli, and some knowledge about evolutionary method.Charter3and4is the core part of the paper. First, we build differentcoupling structure with4,5and much more cells, and found the effect of synchronized transition contact not only closely with the topology of thesystem, but also with whether there exist the ring structures in the system.In particular, both the size and the number of rings have greater effects onsuch transition behavior. Secondly, we introduce synchronization error toqualitative analyze the effect of the topology structure. Furthermore, bycomparing the calculating simulation data, we find that with theincrement of the total number of system cells, there always exist theoptimization structures which have the minimum number of connectingedges in the coupling systems. Above results show that the topologystructures have a very crucial role on synchronization transition incoupled neurons system. Biological system may gradually acquire suchkind of efficient topology structures through the long evolutionary history,thus the systems’information process may be optimized by this scheme.