| Sine60.s of last century, nonlinear science is interestingsubject ofstudying nonlinear phenomenon in many scientific filed, which is said as .third revolution. of natural science in 20 century. Nonlinear dynamics is the one of major research contents of nonlinear science, although many scholars have gotten some accomplishments about it, but for engineering project, there still has a lot of problems to be solved, such as global bifurcation, chaos control and bifurcations control ect. The work in this paperis partial work of.nonlinear dynamics problem in large scale revolution machines (19990510) .supported by the National Natural Science Foundation of China, and supported by National Key Basic Research Special Fund (G 1998020316). The paper is organized as follows: In chapter 1, we have summarized present situation of studying global bifurcation, control chaos as well as control bifurcation by domestic and international scholars, and have grasped newest research development and research technique. We have put forward the research scheme of the paper. In chapter 2, according to Lagrange.s equation, one has established the motion equations of the rigid-flexile couple systems with 1:2 internalresonance,there are square and cubic nonlinearities in nonlinear items. In chapter 3, firstly applyingmulti-scale method, the mean equation with 1:2 internal resonance has been obtained. Secondly, by a series of variable transformations, a near-integrable two-degree-of-freedom Hamiltoniansystem is obtained.When systemic parameters satisfy certain conditions, two saddle points alwaysexist in unperturbedstructure. According to high-dimension Melnikov method, threshold value, which can lead to yield Smale horseshoes, has been investigated by regarding integral as some limits of separate points. In chapter 4, Using the energy-phase criterion, and the fiber clump theory, the necessary condition of existence of Silnikov orbits is determined under Hamiltonian resonance.Numerical simulations have verified the condition. In chapter 5, According to energy-difference functions, energy sequence and pulse III sequence, multi-pulse orbits and homoclinic trees in Hopf-Hopf systems with 1:2 internal resonance have investigated, under Hamiltonian resonance and non-hamiltonian resonance. It is showed that there exists pulse Smale horseshoes in the case of no damping. While in the dissipative case, there exists multi-pulse jumping heteroclinic orbit between of two unstable fixed points of reduced system. In both cases, one can find homoclinic trees, which describe the repeated bifurcations of multi-pulse solutions. Numerical simulations have verified the results. In chapter 6, based on Pyragas method, ones present two modified methods on controlling chaos. The first method is application phase space compressionto original Pyragas method. The second method is the adaptive delayed control by self-feedback, the feedback time and feedback gain can be adaptively determined from current state of controlled system, when switch on controller. As compared with original Pyragas,the adaptive method not only can control system in very short time to the expectation period orbit, but also has stronger ability of counteracting noise. Themethod can applyinto the control of systematic state variables andsystematic parameter. In chapter 7, based on the phase space re-construction theory, ones have studied control chaos in unknown mathematical model of high-dimensional systems.First, the phase space structure can be obtained from the measured signals. Second, the original OJ method has...
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