(2 +1)-dimensional Boussinesq Equation, Chaotic Behavior And Control

Since Lorenz published "Decision on the non-periodic flow" in 1963, non-linear system scientific access to the rapid development, which further reveals the common nature of basic characteristics, the law of sport non-linear system. The found of chaotic motion was extremely important in describing the various types of natural phenomena in power systems, thus nonlinear science can be development rapidly in the last twenty years. That is chaos everywhere, many physical, mechanical problems in the can into a small disturbance with a period with homoclinic orbit or heteroclinic orbit of the second order ordinary differential equations. For such systems can usually be handled by Melnikov method to determine whether there is in the sense of Smale horseshoes in chaotic invariant set.Bifurcation, periodic, homoclinic and chaotic behaviour for (2+1)-Dmensional Boussinesq equation and related issues are studied under perturbation using the Melnikov method, and use positive feedback and coupling feedback method of chaos to control. Chaos arising from subharmonic instability and homoclinic crossings are observed. Both period-doubling bifurcation and the Melnikov sequence of subharmonic bifurcation are found and lead chaotic behaviour. Continuously improve the development of Boussinesq quation-based model with shallow water wave to make it more accurate and effective simulation of natural phenomena in shallow waters.