Analysis Of The Dynamical Behavior Of Coupled Hamiltonian Systems

The nonlinear system exhibits a very complicated dynamics property. There are many various orbits in some systems especially in coupling systems;there will be many kinds of orbits, the orbits are important to study the quantum of non-integral system. There are much research about the particle's movement in the double trap because its complexity, diversity and essentiality in theory currently. The integrability of the system .had changed in essence following the outside force;the fixed circle of the integral system had different topological structure. The text had studied a particle moved in the double trap, which had been added the magnetic. And analyzed the property of the particle moved in the trap which was bound by magnetic, discussed the rule of the particle following the parameters in detail. My article includes two parts:1, Compared with the single system, the coupling system are much more complicated than single system. The model we studied can be regarded as the coupling of duffing oscillator and simple harmonic oscillator in classic. We found that the character of dynamics was decided by the bound potential and the interaction. The key to judge integral or non-integral of Hamiltonian system is look for the independent sport integration the same number as the freedom of the system, but it is difficult to find. What need is to use numerical value to judge. Poincare Surface of Section is one of the basic means to judge chaotic in conservatism system. Chapter two had analyzed the motion of the particle in Poincare Surface of Section, and foundthe regulation of the coupling system following the parameters and the initial conditions: Fixed the initiatory conditions, along with the change of the parameters, we can found that the movement of the particle can exhibit many states, For example, fixing points, periodic, quasi-periodic and chaos. To the specific parameter and different initiatory conditions, According to the Poincare Surface of Section, we know ih^rc are many sport orbits of the particle, and the fixed circle of the integral system had different topological structures.2n Analyzed the time sequence of the coupling system, we can also make sure the property and characteristics of the system. The chapter three did the further analysis to the model using the time sequence. We got the phase space fig, which has the same property as the original system, when selected proper delay time and embed dimension. To the vibration time sequence, we did the Fourier transformation in power spectrum. Judging the change of the sport states following the parameters. The result was consistent with it in Poincare. The two methods made use of the time sequence to analysis the system. So, as long as find out the time sequence of the system, we can analyze the characteristics of the system. The Hamiltonian we studied , the investigation to it and the result we got was a new example in the nonlinear system.