Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor

Abstract

In order to make the peak and offset of the signal meet the requirements of artificial equipment, dynamical analysis and geometric control of the laser system have become indispensable. In this paper, a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system. By using numerical measures, complex dynamical behaviors of the memristive laser system are uncovered. It appears the alternating appearance of quasi-periodic and chaotic oscillations. The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy. Interestingly, initial-values-oriented extreme multi-stability patterns are found, where the coexisting attractors have the same Lyapunov exponents. In addition, the introduction of a memristor greatly improves the complexity of the laser system. Moreover, to control the amplitude and offset of the chaotic signal, two kinds of geometric control methods including amplitude control and rotation control are designed. The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics. Finally, a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.