Synchronization Analysis in Models of Coupled Oscillators - Toso, Guilherme [UNESP] (2020)
The present work deals with the analysis of the synchronization possibility in chaotic oscillators, either completely or per phase, using a coupling force among them, so they can be used in attention systems. The neural models used were Hodgkin-Huxley, Hindmarsh-Rose, Integrate-and-Fire, and Spike-Response-Model. Discrete models such as Aihara, Rulkov, Izhikevic, and Courbage-Nekorkin-Vdovin were also evaluated. The dynamical systems’ parameters were varied in the search for chaos, by analyzing trajectories and bifurcation diagrams. Then, a coupling term was added to the models to analyze synchronization in a couple, a vector, and a lattice of oscillators. Later, a lattice with variable parameters is used to simulate different biological neurons. Discrete models did not synchronize in vectors and lattices, but the continuous models were successful in all stages, including the Spike Response Model, which synchronized without the use of a coupling force, only by the synchronous time arrival of presynaptic stimuli. However, this model did not show chaotic characteristics. Finally, in the models in which the previous results were satisfactory, lattices were studied where the coupling force between neurons varied in a non-random way, forming clusters of oscillators with strong coupling to each other, and low coupling with others. The possibility of identifying the clusters was observed in the trajectories and phase differences among all neurons in the reticulum detecting where it occurred and where there was no synchronization. Also, the average execution time of the last stage showed that the fastest model is the Integrate-and-Fire.