Theoretical Analysis on Wave Dynamics in Cellular Chaotic Neural Networks
楊 李 · Institutional Repositories DataBase (IRDB) · 2018
Wave dynamics emerge widely in spatially extended dynamical systems, including biological and artificial neural networks.This thesis investigates the wave dynamics in a cellular chaotic neural network (CNN) under simplified settings, dealing with both characterization and control of waves.Specifically, the plane wave dynamics is studied from the point of view of local bifurcation theory with an emphasis on the Bogdanov-Takens (BT) bifur-waves in the network, which demonstrate amplitude reduction near the phase singularity.A DPSC method is proposed for eliminating the spiral waves, where a control signal is constructed to indicate the presence of spiral waves and a limiting threshold modulated by the control signal is imposed on the refractory internal state of the network.Such a control scheme turns out to be successful in redirecting the network from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state.The pre-, intra-, and post-control dynamics exhibit different characteristics in the frequency domain; the PW-inducing and SO-inducing control processes are also distinct.Furthermore, a partial selectivity of the control results between PW and SO by varying the control parameters is discovered.This scheme surpasses existent methods of removing spiral wave in the sense that not only homogeneous states are produced and that the control does not need to be turned off manually.The results of this thesis provide fundamentals of the traveling wave dynamics in the cellular CNN and may help to facilitate the future application of such networks.These results may also be beneficial to the study of wave dynamics in other spatially extended dynamical systems.