Justin Mibaile

By Mibaile Justin, Malwe Boudoue Hubert, Gambo Betchewe, Serge Yamigno Doka and Kofane Timoleon Crepin

From a theoretical equation, modeling the dynamic of the time-dependent coefficients of the first and the second Karhunen-Loeve (KL) expansion of a superconducting quantum interference device (SQUID) signal, chaotic phase transition has been studied in the human brain. Through numerical investigations, the bifurcation diagram and the dynamic of Lyapunov exponent have been plotted. These diagrams reveal that throughout the variation of the control parameter here the frequency of the acoustic stimulus, the brain bifurcates from chaotic states to periodic or to quasiperiodic one. Also a chaotic phase portrait of the KL modes and its corresponding Poincaré section have been plotted. The origin of chaos in the human brain could be due to the self-organizing processes of nonequilibrium phase transition occurring in the electrochemical physiological phenomena of the complex nerve cells and neural assembly. Besides, the occurrence of chaos in the absence of stimuli has been remarked and thought to be due to the fact that an intrinsic brain could be chaotic. Moreover it has been found that the range of frequency for which the brain is forced to behave periodically could be harmful to the thinking process.

Part of the book: Research Advances in Chaos Theory