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Role of Nonlinear Dynamics in Endocrine Feedback
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Authors: Chinmoy K. Bose (St. Bartholomew's Hospital, London, UK) 
Book Description:
Endocrine feedback system may not be appreciated by conventional hormone level estimation at a single point of time. Our body also needs to be looked at as a dynamical system, a dissipative structure. Specifically, the information processing at the neuroendocrine level must be guided by a science that is not random but deterministic. For sustenance of life body environ must always (at the present moment) balance itself delicately and relentlessly. In this dynamical system, feedback control will essentially be mathematical control that has to be understood in the light of physical control theory. Whatever goes around inside the body must be originating from chemical reactions, but factors controlling the nature and rate and limit of those reactions are multi-relation oriented. The outcome of such relationship is not limited to linear reactions but dependent on some “non-material entity”, like balancing while cycling or walking on a rope. This non-material entity is described as “feedback” relationship. This book tries to elucidate how and why such kind of relationship must be understood in order to know this reportedly simple subject of endocrine feedback.

Table of Contents:
Preface

Acknowledgement

Foreword
Abbreviation

Chapter 1. History of Endocrine and feedback;pp. 1-127
1 Introduction 10
1.1 History of Endocrinology 11
1.2 Endocrine disease 33
1.3 Evolution of feedback concept in endocrinology 35
1.4 Feedback: modern text 44
1.5 Homeostasis 49
1.6 Scientists, mathematicians and evolution of feedback science 71
1.7 Cybernetics 175
1.7.1 Servomechanisms 177
1.7.6 Sociology and Sociocybernetics 184
1.7.7 System dynamics 185
1.7.8 Systems engineering 186
1.7.9 Systems psychology 187
1.7.10 Systems and "Systems theory" 187
1.7.11 The Roots of Cybernetic theory 190
1.7.12 Teleology 203
1.8 Systems theory, cybernetic and politics 216
1.9 Feedback, World War II, and Filters 227
1.10 Cybernetics in post war 230
1.11 Nonlinear science and Lorenz 237

Chapter 2. Models;pp. 129-162
2. Mathematical models in physiology 258
2.1 Physiological Systems via Mathematical Models 262
2.2 Mathematical biology 268
2.3 mathematical modeling in fifties 272
2.4 Classical models up to eighties 281
2.5 Evolution and maturity in statistics 292
2.6 Basic principles of dynamical systems 299

Chapter 3. Nonlinearity;pp. 163-242
3. Nonlinear Dynamics and Chaos 310
3.1 Basic Concepts 310
3.1.1 Logistic Difference Equation 310
3.1.3 Period doubling 316
3.1.4 Bifurcation Diagram 317
3.1.5 Sensitivity to initial conditions 319
3.1.6 Nonlinear Statistical Tools 321
3.1.6.1 Return Maps 321
3.1.6.2 Types of 'Noise' 323
3.1.6.3 Predator-prey system 325
3.1.6.4 The Buckling column system 328
3.1.7 Glossary 333
3.2 The Three Body Gravitational Problem 337
3.2.1 The Logistic Map 341
3.2.2 The Lorenz Attractor 344
3.2.3 Lyapunov exponents, Lyapunov spectrum and Lyapunov function 350
3.3 General Properties of Lyapunov Exponents 352
3.4 Nonlinear system 356
3.4.1 Nonlinear algebraic equations 357
3.4.2 Nonlinear recurrence relations 357
3.4.3 Nonlinear differential equations 357
3.4.4 Ordinary differential equations 358
3.4.5 Partial differential equations 358
3.4.6 Pendulum 360
3.5 equation of motion 362
3.5.1 The Equation of Motion of an undamped and undriven pendulum 363
3.5.2 Equations of Motion of damped and driven pendula 365
3.5.3 Nonlinear Oscillations 376
3.5.6 Nonlinear Resonance 379
3.5.7 Nonlinear Dynamics 383
3.5.8 Basic Terms of Nonlinear Dynamics 384
3.5.9 Stability and Bifurcation 389
3.5.9.1 Stability 389
3.5.9.2 Bifurcation 392
3.5.10 The Nature of Deterministic Chaos 399
3.6 Chaos theory 414
3.6.1 Chaotic dynamics 420
3.6.2 Attractors 422
3.7 Nonlinear control 426
3.8 Systems biology 430
3.9 Endocrine System 435

Chapter 4. Literature survey: research on nonlinearity in endocrine;pp. 243-282
4. Nonlinearity of endocrine system in literature 444
4.1 introductions 444
4.2 hormone specific works 447
4.2 .1 adrenal, gluco-corticoid 447
4.2.2 Insulin 453
4.2.3 gonadotrophins 465
4.2.4 Thyroid 477
4.2.5 parathormone, calcium 479
4.2.6 Vasopressin 482
4.2.7 Human growth hormone, prolactin 486
4.2.8 hypothalamic-pituitary-adrenal axis 487
4.3 theoretical biology of hormone, hormone receptors 490

Chapter 5. Two articles;pp. 283-342
5.1 Role of nonlinear dynamics in endocrine feedback 519
5.2 Case study: a research article in Commun. Theor. Phys 603

Index

   Series:
      Mathematics Research Developments
   Binding: Hardcover
   Pub. Date: 2009
   Pages: 7 x 10, 369pp.
   ISBN: 978-1-60741-948-8
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Role of Nonlinear Dynamics in Endocrine Feedback