Dynamics of Coupled Heterogeneous Oscillators with Application to Biological Systems

这项研究将考察具有根本不同的基本物理原理的振荡系统的相互作用所产生的行为。振荡器有不同的自然频率和波形。这项工作询问集体行为对振荡器的变化和振荡器之间的通信有多敏感。对耦合非线性振子的研究可以加深对生物系统的理解。物理上不同的生物振荡器尤其令人感兴趣。其他生物振荡器表现出复杂的波形，例如神经元的尖峰。尽管不同的相互作用的生物系统普遍存在，但很少有相关的实验。大多数研究考察一种系统类型内的同质振荡器。学生将接受理解、建模、模拟和实验研究物理上不同的耦合系统的培训。这个项目将进行耦合不同物理振荡器系统的实验。通过这些实验，降维模型的优势和劣势将被揭示出来，这在类似振荡器的系统中可能并不明显。降维模型对于生物振荡器的分析是重要的，因此，对模型的深入了解是重要的。被研究的系统具有不同的振荡动力学，具有相似的生物模式；像心脏一样，光机振荡器可以表现出多种空间模式的振荡，而肺部和光电振荡器则不能。与生物振荡器不同，这些不同的振荡器都有精确的数学模型。因此，这项工作将为不同生物系统之间的相互作用创造一个灵活的实验代理，同时为不同物理性质的同步、延迟耦合和相互作用振子的研究提供理论进步的机会。

This study will examine the behavior that arises from the interactions of oscillating systems with fundamentally different underlying physical principles. The oscillators have different natural rates and wave shapes. The work asks how collective behavior is sensitive to changes in the oscillators and the communications between oscillators. The study of coupled nonlinear oscillators can lead to a deep understanding of biological systems. Physically dissimilar biological oscillators are of particular interest. Other biological oscillators exhibit complex waveforms, such as the spiking of neurons. Despite the prevalence of dissimilar interacting biological systems, there have been few related experiments. Most studies examine homogeneous oscillators within one system type. Students will be trained in understanding, modeling, simulating, and experimentally investigating coupled physically dissimilar systems. This project will perform experiments that couple dissimilar physical oscillator systems. Through these experiments, strengths and weaknesses of reduced-variable models will be revealed that may not be apparent in systems of similar oscillators. Reduced-variable models are important to the analysis of biological oscillators, thus, insights into the models are important. The systems to be studied have different oscillatory dynamics with analogous biological modes; like the heart, an opto-mechanical oscillator can exhibit multiple spatial modes of oscillation while the lungs and an opto-electronic oscillator cannot. Unlike biological oscillators, there are accurate mathematical models for these dissimilar oscillators. Thus, this work will create a flexible experimental proxy for interactions between dissimilar biological systems, while providing an opportunity for theoretical advancements in the study of synchronization, delayed coupling, and interacting oscillators with different physical properties.