Multistability and bifurcations for polyrhythmic Central Pattern Generators

多节奏中心模式发生器的多稳定性和分叉

• 批准号: 1009591
• 负责人: Andrey Shilnikov
• 金额: $ 20.5万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009591&HistoricalAwards=false
• 关键词: Multistability; bifurcations; polyrhythmic; Central; Pattern

The project will develop the dynamical principles of multistability of bursting patterns of polyrhythmic activity and its control for multifunctional Central Pattern Generators. Multistability enhances the flexibility of nervous systems and has far reaching implications for motor control, dynamic memory, information processing, and decision making. The Investigator and his students will identify and study generic nonlocal bifurcations of bursting rhythms in realistic models of single and networked interneurons, as well as create a dynamical systems classification for the bursting genesis in CPGs. The research team will create a suite of new methods and computational tools based on the theory of dynamical systems and global bifurcations to examine complex transformations of bursting patterns in high-order Hodgkin-Huxley type models and networks. The Investigator and his students will enhance the existing mathematical technique by creating transparent computational tools for the detection and prediction of transformations of complex oscillatory solutions in neuronal models with multiple time scales. This includes the novel approaches of reducing neuronal dynamics to a complete, equation-free family of onto Poincaré mappings for membrane potentials, and the phase-difference mappings for bursting CPG circuits. The reduction will yield a clear understanding of the dynamics of a high-order, multiple-time scale neuron model, as well as provide with a control of the multistability by revealing the hidden centers that govern globally the dynamics of a mutlifunctional CPG network. Having the extensive knowledge of dynamical properties of networked busting interneurons will allow the team to derive precise phase models to replicate the dynamics of their high-dimensional models. These reduced models will be used to examine larger and more complex realistic models of the specific excitatory-inhibitory CPG circuits. The ability of distinct anatomical circuits, like Central Pattern Generators, to generate multiple patterns of neural activity to control several locomotion types, like cardiac beating, waking, swimming etc, is widespread among vertebrate and invertebrate species. Understanding generic mechanisms of the evolution of neuronal connectivity and transitions between different patterns of neural activity and modeling these processes are the fundamental challenges for applied mathematics and computational neuroscience. This project is a genuinely cross-disciplinary research, bridging state-of the art mathematics, more specifically the theory of applied dynamical systems and nonlocal bifurcations, with life sciences. It shall extend and generalize our understanding of dynamical principles of neural systems; specifically mechanisms regulating polyrhythms of multifunctional Central Pattern Generators. Multistability enhances the flexibility of nervous systems and has far reaching implications for motor control, dynamic memory, information processing, and decision making of humans and animals. The Investigator and his students will identify and study generic bifurcations of bursting rhythms in realistic models of single and networked interneurons, as well as create a dynamical systems classification for the bursting genesis in multifunctional neural circuits.

该项目将开发多节律活动的突发模式的多稳定性的动力学原理及其对多功能中央模式发生器的控制。多稳态增强了神经系统的灵活性，对运动控制、动态记忆、信息处理和决策有着深远的影响。研究者和他的学生将识别和研究单个和网络化中间神经元的现实模型中爆发节律的一般非局部分叉，并为CPG中的爆发起源创建动力系统分类。 该研究小组将创建一套新的方法和计算工具，基于动力系统和全局分叉的理论，以研究高阶Hodgkin-Huxley型模型和网络中突发模式的复杂变换。研究者和他的学生将通过创建透明的计算工具来增强现有的数学技术，用于检测和预测具有多个时间尺度的神经元模型中复杂振荡解的变换。 这包括新的方法减少神经元动力学到一个完整的，方程自由家庭的庞加莱映射的膜电位，和相位差映射爆裂CPG电路。减少将产生一个清晰的了解高阶，多时间尺度神经元模型的动态，以及提供一个控制的多稳定性，揭示隐藏的中心，全球治理的动态多功能CPG网络。 对网络化破坏的中间神经元的动力学特性有广泛的了解，将使团队能够推导出精确的相位模型，以复制其高维模型的动力学。这些减少的模型将被用来检查更大和更复杂的现实模型的特定兴奋抑制CPG电路。不同的解剖电路（如中央模式发生器）产生多种神经活动模式以控制几种运动类型（如心跳、清醒、游泳等）的能力在脊椎动物和无脊椎动物物种中广泛存在。理解神经元连接的演化和不同神经活动模式之间的转换的一般机制，并对这些过程进行建模是应用数学和计算神经科学的基本挑战。 这个项目是一个真正的跨学科研究，桥梁国家的最先进的数学，更具体地说，应用动力系统和非局部分叉的理论，与生命科学。它将扩展和概括我们对神经系统动力学原理的理解;特别是调节多功能中央模式发生器的多节律的机制。 多稳态增强了神经系统的灵活性，对人类和动物的运动控制、动态记忆、信息处理和决策具有深远的意义。 研究者和他的学生将识别和研究单个和网络化中间神经元的现实模型中爆发节律的一般分叉，并为多功能神经回路中的爆发起源创建动力系统分类。