| Summary: | 碩士 === 國立中央大學 === 生物物理研究所 === 104 === We consider a magnetic dipole (compass needle) under a constant magnetic (Earth's) field and an external sinusoidally oscillating magnetic field (of magnitude B2) that is perpendicular to the former. The angular motion displays complex nonlinear oscillations and undergoes a period-doubling route to chaos. The equation of motion of the system possesses a special symmetry when angle inversion together with time translation of half of the driving period is applied. Due to this symmetry, coexistence of attractors, including symmetric periodic states and symmetric chaotic strange attractors, occurs. The properties of these attractors, such as how the symmetric attractor pairs appear and merge, as revealed by numerical solution of the differential equations and phase portraits, are examined in detail as the parameters of the system change. Interestingly, it is found that in addition to the coexistence of symmetric limit cycle attractor pair (both having the same period state), two different odd-periodic states not related by symmetry, can coexist. In addition, a pair of symmetric period-2 limit cycles and a chaotic attractor can coexist in certain parameter regimes.
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