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Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission. [ABSTRACT FROM AUTHOR]

Analyzing the conditions for generating beta oscillation in basal ganglia plays a key role in understanding the mechanism of Parkinson's disease (PD). In this paper, we consider a Cortex–STN–GPe model, which consists of the external segment of globus pallidus (GPe), subthalamic nucleus (STN) and cortex including excitatory and inhibitory neurons. We obtain the stability boundary conditions for the model through theoretical analyses, and discuss the influence of two inputs to cortex and GPe on oscillations by numerical simulation. Our results reveal that the model can oscillate for large connection weight between STN and GPe, much larger input to the cortex, and most input values to the GPe. Furthermore, the effects of parameters in the cortical circuit on the amplitude and frequency of the beta oscillation are analyzed. We show that larger delay and larger firing rate of excitatory and inhibitory neurons in the cortex make the model oscillate easily. We hope that our results will be helpful for further understanding the mechanisms of beta oscillations in the treatment of Parkinson's disease and may apply to some studies of neural oscillations. [ABSTRACT FROM AUTHOR]