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In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.

Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen's chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

A simplified structure of birefringent chalcogenide As2Se3 photonic crystal fiber (PCF) is designed. Properties of birefringence, polarization extinction ratio, chromatic dispersion, nonlinear coefficient, and transmission are studied by using the multipole method, the finite-difference beam propagation method, and the adaptive split-step Fourier method. Considering that the zero dispersion wavelength of our proposed fiber is about 4 μm, we have analysed the mechanism of spectral broadening in PCFs with different pitches in detail, with femtosecond pulses at a wavelength of 4 μm as the pump pulses. Especially, mid-infrared broadband polarized supercontinuums are obtained in a 3-cm PCF with an optimal pitch of 2 μm. Their spectral width at −20 dB reaches up to 12 μm. In the birefringent PCF, we find that the supercontinuum generation changes with the pump alignment angle. Research results show that no coupling between eigenpolarization modes are observed at the maximum average power (i.e., 37 mW), which indicates that the polarization state is well maintained.