Rhythm oscillation in fractional-order Relaxation oscillator and its application in image enhancement

The existence of limit cycles ensures that the dynamic systems generate a rhythmic oscillation phenomenon. In this paper, the investigation of limit cycles in the fractional-order Relaxation oscillator was demonstrated by analysis of the stability domains, and the simulation of the cortex rhythms was implemented based on the fractional-order Relaxation model. When the fractional-order Relaxation oscillator oscillates in rhythm, the Quasi Gamma Curve (QGC) Model was established. The proposed QGC Model was applied to enhance images. The performance of image enhancement based on QGC model was improved compared with the Gamma correction curve and the Retinex algorithm.