Abstract
Rhythmic behavior is widely present in living organisms. The rhythms can be innate and usually they are externally stimulated by the environment. One such stimulus is the 24 h natural lightdark cycle which governs the activityinactivity cycle of many plants, animals and humans. The cells in the suprachiasmatic nucleus that govern our circadian rhythms are ideally regarded as a group of biological oscillators. In the Winfree model, the biological oscillators are regarded as coupled oscillators. The Winfree model was used to describe the synchronization of a large system of globally coupled phase oscillators. Considering that external stimuli and environmental factors, such as the change of light and darkness, have great influence on the rhythmic behavior, a periodic forcing is added to Winfree system.
The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of nonidentical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The OttAntonsen is used to give a lowdimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and nondetuned cases for identical oscillators and understand the entrainment patterns using stability theory.
The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of nonidentical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The OttAntonsen is used to give a lowdimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and nondetuned cases for identical oscillators and understand the entrainment patterns using stability theory.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  9Nov2020 
Place of Publication  [Groningen] 
Publisher  
DOIs  
Publication status  Published  2020 