Entrainment in forced Winfree systems

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 light-dark cycle which governs the activity-inactivity 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 non-identical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The Ott-Antonsen is used to give a low-dimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and non-detuned cases for identical oscillators and understand the entrainment patterns using stability theory

A STUDY ON DYNAMIC SYSTEMS RESPONSE OF THE PERFORMANCE CHARACTERISTICS OF SOME MAJOR BIOPHYSICAL SYSTEMS

Dynamic responses of biophysical systems - performance characteristic

Rhythmic Action Synchronizes Memory Replay During Reinforcement Learning

Our cognitive abilities - learning from the past, sensing the current environment, planning into the future, executing an action, and infusing value into an experience - all rely on precisely timed and widespread electrical communications across neural networks. The brain’s hippocampal formation receives multimodal input, forges episodic associations, and predicts future state. Oscillating electrical bursts originating from the hippocampus, termed ‘sharp-wave ripples’ (SWR), often contain patterns of previously expressed neural spike sequences, and are necessary for certain forms of learning and memory. The discharge of SWR-replay resonates in remote parts of the brain and displays specific characteristics depending on a subject’s state of awareness and sensory context. In the sleep state, when motoric repertoire is limited, waves of breathing synchronize neural activity in several regions of the brain, including SWRs of the hippocampus. During active sensation of the awake state, cyclic licking dynamically entrains taste-reward networks in subcortical and cortical areas throughout learning. However, the neural correlates linking oromotor movements in the active learning state to the memory system of the hippocampal formation have not yet been established. Given the recurrence of SWR-replay during rhythmic ingestion of reinforcement learning and the hierarchical coupling of orofacial behaviors, we hypothesized that repeated licking could provide the oscillatory framework to synchronize memory reactivation during active learning. We approach this question with new technology development to track licking events at a reward port (P-event) during behavior on a spatial alternation task. Additionally, we developed a modular brain implant to simultaneously record from hippocampal area CA1 and medial entorhinal cortex (MEC) - interconnected brain regions that are crucial to episodic memory processing. Along with the co-modulation of individual neurons by licking and SWRs, we provide the first evidence that SWRs detected in dorsal CA1 synchronize with the phase of P-event cycle during learning. Furthermore, we confirmed that SWRs occurring during licking bouts contain neural reactivation of active navigation and trigger enhanced ripple-frequency power in downstream MEC. These results connect movement with memory and may assist in addressing abnormal ingestion behaviors that negatively affect mental or physical healt