Functional Aspects of Chaotic Dynamics in A Recurrent Neural Network Model, Theory, Applications, and Hardware Implementation
Yongtao Li · Institutional Repositories DataBase (IRDB) · 2010
Chapter 1 Introduction.This chapter presents the research background and the motivation.It comprises the understanding of brain as complex systems, the proposal of somehow harnessing the onset of chaos, and ill-posed problems that are taken as functional experiments based on this ideas.Finally, the thesis is outlined.Chapter 2 Chaos and Dynamical Systems.This chapter gives a brief review of basic ideas and terminology in the theory of dynamical systems.Along our aim to introduce several topics of chaos, intrinsic properties of chaos are discussed and demonstrated by using several typical discrete dynamical systems.Chapter 3 Neural Networks.This chapter begins with a brief review of artificial neural networks, and how to embed memory patterns into a recurrent neural network model (RNNM) is highlighted.An orthogonalized learning method to effectively embed memory cycles into RNNM is discussed in detail.Chapter 4 Chaotic Dynamics in RNNM.After several memory cycles are embedded using the orthogonalized learning method, the performance of associative memory is evaluated by means of calculating an approximate basin volume via statistical method.Chaotic dynamics is introduced into RNNM by changing a system parameter, connectivity.The route from attractor to chaotic dynamics is analyzed by means of calculating bifurcation diagram and basin visiting measure. Chapter 5 Chaos and Adaptive Control.This chapter addresses how chaos is applied to solving ill-posed problems in control tasks.A simple coding method, called motion functions are proposed so that complex dynamics with many but finite degrees of freedom in a high dimensional state space can be utilized to generate low dimensional complex motions.In terms of the motion functions, several prototype simple motions are embedded into RNNM.In turn, by the coding of motion functions, chaotic dynamics in RNNM correspondingly generates chaotic motion.A novel idea, adaptive switching of connectivity, was proposed for the application of chaotic dynamics in solving ill-posed problems.Using this idea, chaotic dynamics in RNNM is applied to solving two ill-posed problems in control tasks.Computer experiments on controlling an object to solve two-dimensional mazes and to track a moving target are successfully implemented.And then we have evaluated the performance of solving these problems using chaotic dynamics in RNNM. Chapter 6 Hardware Implementation into An Autonomous Robot.This chapter presents how to implement those functional experiments into hardware.The construction of control system is addressed and a robot is designed and built.The robot driven by complex dynamics generated by a neuro-chaos simulator, which functions as brainmorphic device to simulate a RNNM.Those functional experiments were implemented successfully.Chapter 7 Quasi-layered RNNM.This chapter presents a quasi-layered RNNM consisting of sensory neurons and motor neurons, which gives a biologically realistic meaning.The inherent properties of quasi-layered RNNM are analyzed by bifurcation diagram.By virtue of sensitive response of chaos, while sensory neurons respond to external signals sensitively, motor neurons respond to sensory neurons sensitively.Thus, chaotic dynamics is introduced in both sensory neurons and motor neurons.Inspired by neurobiology, presynaptic inhibition is introduced and provides the robot with naturally adaptive behaviors.Finally, functional experiments were implemented successfully in computer experiments and hardware implementation.Chapter 8 Functional Investigation of Chaotic Neurons.This chapter presents chaotic neural network consisting of neurons with continuous states in order to confirm that the functional features of chaos do not depend on the detailed structure of models.Adaptive switching of parameters results in adaptive motions.Computer experiments on controlling an object to solve two-dimensional mazes are successfully implemented. Chapter 9 Summary and Concluding Remarks.This chapter presents the conclusions of this thesis, and recommendations for future work.Appendix A and Appendix B present the relevant information on designing the sensory system of the robot and wireless communication interface between neuro-chaos simulator and the robot in Chapter 6.This is followed by bibliography.