外磁场中带电托马斯振子的动力学
Dynamics of a Charged Thomas Oscillator in an External Magnetic Field
摘要：
在这封信中，我们提供了一个详细的数值检查的动力学带电托马斯振荡器在外部磁场。我们采用循环对称的托马斯振子，然后对其进行修改，来研究带电粒子在外部磁场中的动力学。这些动力学行为的弱和强的场强参数属于两类;保守和耗散。该系统表现出一个复杂的准周期吸引子，其拓扑结构依赖于保守制度中的高场强的初始条件。随着场强参数的减小，系统从绝热运动向混沌运动转变。在耗散状态下，系统在弱磁场和弱阻尼下是混沌的，但在高磁场下则表现出极限环。这种行为是由于一个额外的负反馈回路，在高场强下开始起作用，并迫使系统动力学在周期振荡中保持稳定。在弱阻尼和弱场强条件下，系统动力学通过混沌行走模拟布朗运动。
英文摘要：
In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the dynamics of a charged particle in an external magnetic field. These dynamical behaviours for weak and strong field strength parameters fall under two categories; conservative and dissipative. The system shows a complex quasi-periodic attractor whose topology depends on initial conditions for high field strengths in the conservative regime. There is a transition from adiabatic motion to chaos on decreasing the field strength parameter. In the dissipative regime, the system is chaotic for weak field strength and weak damping but shows a limit cycle for high field strengths. Such behaviour is due to an additional negative feedback loop that comes into action at high field strengths and forces the system dynamics to be stable in periodic oscillations. For weak damping and weak field strength, the system dynamics mimic Brownian motion via chaotic walks.
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