Bifurcation Analysis On The Class-B Lasers Model With One Delay

Laser technology has become an integral part of science and technology and it will become more and more important with our social developing. The basic theory of laser technology comes from one of Einstein's published papers named Quantum theory of radiation in 1917. After more than 40 years of research, the first laser was produced in 1960 called ruby laser. Subsequently it attracted large numbers of researchers. Laser has many unique features campared to ordinary light: high selective, high monochromatic, high coherent and so on. Today, laser technology has play a role in promoting many subjects'development such as physics, chemistry, medicine and so on. The laser technology has play a key role on various industries in our society. So it's very worth of our study on the laser system and it has a very important social value. There are many kinds of lasers. Similarly there are many kinds classifications. But the main reserch in this paper is on B class laser, such as semiconductor lasers and CO₂ laser.The main task of this article is that: first, we study the class B laser model with time delay to get the stability of the fixed points and prove that when the parameter is a certain critical value, the system experience Hopf bifurcation. Second, we study the Hopf bifurcation of the system and get the exact information of it, such as the stability of the periodic solution and the direction of the periodic solutions. Finally, we use the numerical simulation to support the theoretical results.