具有分数维、时滞和同步的复杂系统

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基本信息

书名:具有分数维、时滞和同步的复杂系统

作者:罗朝俊,孙建桥

出版社：高等教育出版社

出版日期：2011-01-01

ISBN：9787040297102

字数：580000

页码：370

版次：1

装帧：精装

开本：16开

商品重量：0.001kg

编辑推荐

内容提要

Complex Systems Fractionality， Time-delay and Synchronizatiocovers the most recent developments： and advances ithe theory and applicatioof plex Systems ithese areas， Each chapter was writteby scientists highly active ithe field ofplexsystemS. ebook discusses a new treatise ofractional dynamics and control， as well as the new meth0ds f0r differential delay systems and control，Lastly， a theoretical framework for the plety and synchronizatioofplex system is presented.
The book is intended for researchers ithe field of nonlinear dynamics imathematics， physics and engineering， If caalso Serve as a reference book for graduate students iapplied mathematics， physics and engineering.

目录

1 New Treatise iFractional Dynamics
Dumitru Baleanu
1.1 Introduction
1.2 Basic definitions and properties of fractional derivatives and integrals
1.3 Fractional variational principles and their applications
1.3.1 Fractional Euler-Lagrange equations for discrete systems..
1.3.2 Fractional Hamiltoniaformulation
1.3.3 Lagrangiaformulatioof field systems with fractional derivatives
1.4 Fractional optimal control formulation
1.4.1 Example
1.5 Fractional calculus inuclear magic resonance
1.6 Fractional wavelet method and its applications idrug analysis
References

2 Realizatioof Fractional-Order Controllers： Analysis， Synthesis and Applicatioto the Velocity Control of a Servo System
Ramiro S. Barbosa， Isabel S. Jesus， Manuel F. Silva，
J.A. Tenreiro Machado
2.1 Introduction
2.2 Fractional-order control systems
2.2.1 Basic theory
2.2.2 Fractional-Order controllers and their implementation
2.3 Oustaloups frequency appromatiomethod
2.4 The experimental modular servo system
2.5 Mathematical modelling and identificatioof the servo system
2.6 Fractional-order real-time control system
2.7 Ziegler-Nichols tuning rules
2.7.1 Ziegler-Nichols tuning rules： quarter decay ratio
2.7.2 Ziegler-Nichols tuning rules： oscillatory behavior
2.7.3 Comments othe results
2.8 A simple analytical method for tuning fractional-order controllers
2.8.1 The proposed analytical tuning method
2.9 Applicatioof optimal fractional-order controllers
2.9.1 Tuning of the PID and PIz D controllers
2.10 Conclusions
References

3 Differential-Delay Equations
Richard Rand
3.1 Introduction
3.2 Stability of equilibrium
3.3 Lindstedts method
3.4 Hopf bifurcatioformula
3.4.1 Example 1
3.4.2 Derivation
3.4.3 Example 2
3.4.4 Discussion
3.5 Transient behavior
3.5.1 Example
3.5.2 Exact solution
3.5.3 Two variable expansiomethod （also knowas multiple scales）
3.5.4 Approach to limit cycle
3.6 Center manifold analysis
3.6.1 Appendix： The adjoint operator A
3.7 Applicatioto gene expression
3.7.1 Stability of equilibrium
3.7.2 Lindstedts method
3.7.3 Numerical example
3.8 Exercises
References

4 Analysis and Control of Deterministic and Stochastic Dynamical Systems with Time Delay
Jian-Qiao Sun， Bo Song
4.1 Introduction
4.1.1 Deterministic systems
4.1.2 Stochastic systems
4.1.3 Methods of solution
4.1.4 Outline of the chapter
4.2 Abstract Cauchy problem for DDE
4.2.1 Convergence with Chebyshev nodes
4.3 Method of semi-discretization
4.3.1 General time-varying systems
4.3.2 Feedback controls
4.3.3 Analysis of the method of semi-discretization
4.3.4 High order control
4.3.5 Optimal estimation
4.3.6 Comparisoof semi-discretizatioand higher order control
4.4 Method of continuous time appromation
4.4.1 Control problem formulations
4.5 Spectral properties of the CTA method
4.5.1 A low-pass filter based CTA method
4.5.2 Example of a first order linear system
4.6 Stability studies of time delay systems
4.6.1 Stability with Lyapunov-Krasovskii functional
4.6.2 Stability with Pad6 appromation
4.6.3 Stability with semi-discretization
4.6.4 Stability of a second order LTI system
4.7 Control of LTI systems
4.8 Control of the Mathieu system
4.9 Aexperimental validation
4.10 Supervisory control
4.10.1 Supervisory Control of the LTI System
4.10.2 Supervisory control of the periodic system
4.11 Method of semi-discretizatiofor stochastic systems
4.11.1 Mathematical background
4.11.2 Stability analysis
4.12 Method of finite-dimensional markov process （FDMP）
4.12.1 Fokker-Planck-kolmogorov （FPK） equation
4.12.2 Moment equations
4.12.3 Reliability
4.12.4 First-passage time probability
4.12.5 Pontryagin-Vitt equations
4.13 Analysis of stochastic systems with time delay
4.13.1 Stability of second order stochastic systems
4.13.2 One Dimensional Nonlinear System
References

5 Synchronizatioof Dynamical Systems iSense of Metric Functionals of Specific Constraints
Albert C.J. Luo
5.1 Introduction
5.2 System synchronization
5.2.1 Synchronizatioof slave and master systems
5.2.2 Generalized synchronization
5.2.3 Resultant dynamical systems
5.2.4 Metric functionals
5.3 Single-constraint synchronization
5.3.1 Synchronicity
5.3.2 Singularity to constraint
5.3.3 Synchronicity with singularity
5.3.4 Higher-order singularity
5.3.5 Synchronizatioto constraint
5.3.6 Desynchronizatioto constraint
5.3.7 Peratioto constraint
5.4 Multiple-constraint synchronization
5.4.1 Synchronicity to multiple-constraints
5.4.2 Singularity to constraints
5.4.3 Synchronicity with singularity to multiple constraints
5.4.4 Higher-order singularity to constraints
5.4.5 Synchronizatioto all constraints
5.4.6 Desynchronizatioto all constraints
5.4.7 Peratioto all constraints
5.4.8 Synchronization-desynchronization-peration
5.5 Conclusions
References

6 The Complety iActivity of Biological Neurons
Yong Xie， Jian-Xue Xu
6.1 Complicated firing patterns ibiological neurons
6.1.1 Time series of membrane potential
6.1.2 Firing patterns： spiking and bursting
6.2 Mathematical models
6.2.1 HH model
6.2.2 FitzHugh-Nagumo model
6.2.3 Hindmarsh-Rose model
6.3 Nonlinear mechanisms of firing patterns
6.3.1 Dynamical mechanisms underlying Type I excitability and Type II excitability
6.3.2 Dynamical mechanism for the onset of firing ithe HH model
6.3.3 Type I excitability and Type II excitability displayed ithe Morris-Lecar model
6.3.4 Change itypes of neuronal excitability via bifurcatiocontrol
6.3.5 Bursting and its topological classification
6.3.6 Bifurcation， chaos and Crisis
6.4 Sensitive responsiveness of aperiodic firing neurons to external
stimuli
6.4.1 Experimental phenomena
6.4.2 Nonlinear mechanisms
6.5 Synchronizatiobetweeneurons
6.5.1 Significance of synchronizatioithe nervous system
6.5.2 Coupling： electrical coupling and chemical coupling
6.6 Role of noise ithe nervous system
6.6.1 Constructive role： stochastic resonance and coherence resonance
6.6.2 Stochastic resonance： Whedoes it not occur ineuronal models？
6.6.3 Global dynamics and stochastic resonance of the forced FitzHugh-Nagumo neuromodel
6.6.4 A novel dynamical mechanism of neural excitability for integer multiple spiking
6.6.5 A Further Insight into Stochastic Resonance iaIntegrate-and-fire Neurowith Noisy Periodic Input
6.6.6 Signal-to-noise ratio gaiof a noisy neurothat transmits subthreshold periodic spike trains
6.6.7 Mechanism of bifurcation-dependent coherence resonance of Morris-Lecar Model
6.7 Analysis of time series of interspike intervals
6.7.1 Returmap
6.7.2 Phase space reconstruction
6.7.3 Extractioof unstable periodic orbits
6.7.4 Nonlinear predictioand surrogate data methods
6.7.5 Nonlinear characteristic numbers
6.8 Application
6.9 Conclusions
References

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