论文标题
在两种相互作用的超声对比剂的模型中同步振荡和对称破坏
Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents
论文作者
论文摘要
我们研究了两个耦合振荡器系统中的非线性动力学，描述了两种相互作用的微泡对比剂的运动。在相同的气泡的情况下，方程式系统的相应对称性导致存在渐近稳定同步振荡的可能性。但是，可能很难创建绝对相同的气泡，而且，在实验方案中，对于气泡平衡半径的扰动而言，人们可以观察到。因此，我们研究了各种同步和异步动力学方案的稳定性，相对于这种对称性的破裂。我们表明，确定同步吸引子的稳定性或不稳定性的主要因素是存在/不存在和与同步吸引子共存的异步吸引子的类型。另一方面，在我们研究的所有情况下，异步过度交流吸引子相对于对称性破裂是稳定的。因此，在物理上现实的情景中可能会观察到它们，并且当需要混乱的行为时，可能对合适的应用有益。
We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations leads to the possibility of existence of asymptotically stable synchronous oscillations. However, it may be difficult to create absolutely identical bubbles and, moreover, one can observe in experiments regimes that are unstable with respect to perturbations of equilibrium radii of bubbles. Therefore, we investigate the stability of various synchronous and asynchronous dynamical regimes with respect to the breaking of this symmetry. We show that the main factors determining stability or instability of a synchronous attractor are the presence/absence and the type of an asynchronous attractor coexisting with the synchronous attractor. On the other hand, asynchronous hyperchaotic attractors are stable with respect to the symmetry breaking in all the situations we have studied. Therefore, they are likely to be observed in physically realistic scenarios and can be beneficial for suitable applications when chaotic behavior is desirable.
