Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.

A recurrent wavelet first-order neural network (RWFONN) is proposed to select a desired attractor in a multistable erbium-doped fiber laser (EDFL). A filtered error algorithm is used to classify coexisting EDFL states and train RWFONN. The design of the intracavity laser power controller is developed according to the RWFONN states with the block control linearization technique and the super-twisting control algorithm. Closed-loop stability analysis is performed using the boundedness of synaptic weights. The efficiency of the control method is demonstrated through numerical simulations.

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In this work, a neural super-twisting algorithm is applied to the design of a controller for a flywheel energy storage system (FESS) emulator. Emulation of the FESS is achieved through driving a Permanent Magnet Synchronous Machine (PMSM) coupled to a shaft to shaft DC-motor. The emulation of the FESS is carried out by controlling the velocity of the PMSM in the energy storage stag and then by controlling the DC-motor velocity in the energy feedback stage, where the plant’s states of both electrical machines are identified via a neural network. For the neural identification, a Recurrent Wavelet First-Order Neural Network (RWFONN) is proposed. For the design of the velocity controller, a super-twisting algorithm is applied by using a sliding surface as the argument; the latter is designed based on the states of the RWFONN, in combination with the block control linearization technique to the control of the angular velocity from both machines in their respective operation stage. The RWFONN is trained online using the filtered error algorithm. Closed-loop stability analysis is included when assuming boundedness of the synaptic weights. The results obtained from Matlab/Simulink validate the performance of the proposal in the control of an FESS.