Multistability and bifurcations for polyrhythmic Central Pattern Generators

Georgia State University Research Foundation, Inc., Atlanta GA

Investigators

Abstract

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.