标题： 控制复杂节律：一种分层方法用于极限环切换 显示英文标题

标题： Controlling complex rhythms: A hierarchical approach to limit cycle switching

摘要： 极限环是在相空间中自持的闭合轨迹，表示非线性动力系统中的（不）稳定周期行为。 它们支撑着多种自然现象，从神经元放电模式到工程振荡。 多个同心极限环的存在反映了系统内部的不同行为对称性。 在本工作中，我们研究了由振荡激励驱动的从一个极限环到另一个极限环的分层动力学转变，同时保持其他系统特性。 我们证明，通过分层、分步的周期调制控制多节奏性，可以可靠地在节奏状态之间切换。 这种分层控制框架在神经工程和合成生物学应用中至关重要，其中对复杂节奏行为的精确、鲁棒调制可增强系统功能和适应性。 显示英文摘要

摘要： Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering oscillations. The presence of multiple concentric limit cycles reflects distinct behavioral symmetries within a system. In this work, we investigate the hierarchical dynamical transitions from one limit cycle to another, driven by oscillatory excitation while preserving other system properties. We demonstrate that controlling multirhythmicity through hierarchical, stepwise periodic modulation enables reliable switching between rhythmic states. This hierarchical control framework is crucial for applications in neuro-engineering and synthetic biology, where precise, robust modulation of complex rhythmic behaviors enhances system functionality and adaptability.