Atjaunināt sīkdatņu piekrišanu

E-grāmata: Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues

(Univ Of California, Irvine, Usa)
  • Formāts: 400 pages
  • Izdošanas datums: 16-Aug-2017
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813143357
Citas grāmatas par šo tēmu:
  • Formāts - PDF+DRM
  • Cena: 61,99 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Dynamical System Models In The Life Sciences And Their Underlying Scientific IssuesPalielināt
  • Formāts: 400 pages
  • Izdošanas datums: 16-Aug-2017
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813143357
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) The case study approach focusing on different specific modeling problems familiar to the particular author, and 2) The methods approach teaching some useful mathematical techniques accessible to the targeted student cohort with different models introduced to illustrate the application of the methods taught. The goal and approach of this new text differ from these two conventional approaches in that its emphasis is on the scientific issues that prompt the mathematical modeling and analysis of a particular phenomenon. For example, in the study of a fish population, we may be interested in the growth and evolution of the population, whether the natural growth or harvested population reaches a steady state (equilibrium or periodically changing) population in a particular environment, is a steady state stable or unstable with respect to a small perturbation from the equilibrium state, whether a small change in the environment would lead to a catastrophic change, etc. Each of these scientific issues requires the introduction of a different kind of model and a different set of mathematical tools to extract information about the same biological organisms or phenomena.Volume I of this three volume set limits its scope to phenomena and scientific issues that can be modeled by ordinary differential equations (ODE) that govern the evolution of the phenomena with time. The scientific issues involved include evolution, equilibrium, stability, bifurcation, feedback, optimization and control. Scientific issues such as signal and wave propagation, diffusion, and shock formation pertaining to phenomena involving spatial dynamics are to be modeled by partial differential equations (PDE) and will be treated in Volume II. Scientific issues involving randomness and uncertainty are deferred to Volume III.
Preface xvii
1 Mathematical Models and the Modeling Cycle
1(8)
1.1 Mathematical Models
1(1)
1.2 The Modeling Cycle
2(2)
1.2.1 Formulation
3(1)
1.2.2 Analysis
3(1)
1.2.3 Validation
3(1)
1.2.4 Improved formulation
4(1)
1.2.5 The cycle
4(1)
1.3 Scientific Issues
4(2)
1.4 Scales of Biological Phenomena
6(1)
1.5 Let's Get Started
7(2)
Part
1. Growth of a Population		 9(42)
2 Evolution and Equilibrium
11(16)
2.1 Growth without Immigration
11(4)
2.1.1 Population size dependent growth rates
11(2)
2.1.2 Solution of the model ODE
13(1)
2.1.3 Initial condition and the initial value problem
14(1)
2.2 Exponential Growth
15(2)
2.2.1 Linear growth rate
15(1)
2.2.2 The growth rate constant
16(1)
2.2.3 Model validation
16(1)
2.2.4 Prediction of future population
17(1)
2.3 Estimation of System Parameters
17(4)
2.3.1 The least squares fit
17(1)
2.3.2 The least squares method for exponential growth
18(3)
2.4 A Constant Growth Rate Model
21(1)
2.5 Intravenous Drug Infusion
22(3)
2.5.1 Questions on hypoglycemia
22(1)
2.5.2 Linear models with immigration
22(1)
2.5.3 Mathematical analysis
23(1)
2.5.4 Model improvements
24(1)
2.6 Mosquito Population with Bio-Control
25(2)
2.6.1 The problem of mosquito eradication
25(1)
2.6.2 Constant rate of eradication
26(1)
2.6.3 Seasonal varying growth rate
26(1)
3 Stability and Bifurcation
27(24)
3.1 The Logistic Growth Model
27(3)
3.1.1 Taylor polynomials for the growth function
27(2)
3.1.2 Normalization and exact solution
29(1)
3.1.3 Implication of the exact solution
29(1)
3.1.4 Validation and model improvement
30(1)
3.2 Critical Points and Their Stability
30(7)
3.2.1 Critical points of autonomous ODE
30(2)
3.2.2 Stability of a critical point
32(2)
3.2.3 Graphical method for critical points and their stability
34(2)
3.2.4 Linear stability analysis
36(1)
3.3 Over-fishing of a Commercial Fish Population
37(4)
3.3.1 Fish harvesting
37(2)
3.3.2 Critical points and their stability
39(1)
3.3.3 Bifurcation for fish harvesting
40(1)
3.4 Bifurcation
41(7)
3.4.1 Bifurcation diagram and horizontal tangency
41(2)
3.4.2 Basic bifurcation types
43(5)
3.5 Structural Stability and Hyperbolic Points
48(3)
Part
2. Interacting Populations		 51(108)
4 Linear Interactions
53(28)
4.1 Types of Interaction
53(1)
4.2 Red Blood Cell Production
54(4)
4.2.1 Model formulation
54(1)
4.2.2 Method of elimination
55(1)
4.2.3 Implication of mathematical results
56(2)
4.3 Linear Systems with Constant Coefficients
58(10)
4.3.1 Vector form
58(1)
4.3.2 Complementary solutions
59(1)
4.3.3 Fundamental matrix solution
59(4)
4.3.4 Matrix diagonalization
63(1)
4.3.5 De-coupling of the linear system
63(2)
4.3.6 The matrix exponential
65(1)
4.3.7 Symmetric matrices
66(2)
4.4 DNA Mutation
68(5)
4.4.1 The double helix
68(1)
4.4.2 Mutation due to base substitutions
69(1)
4.4.3 Linear model
70(1)
4.4.4 Equal opportunity substitution
70(3)
4.5 Defective Matrices
73(8)
4.5.1 A simple example
73(2)
4.5.2 Systematic reduction to Jordan form
75(1)
4.5.3 Matrices with a single eigenvector
75(2)
4.5.4 Multiple but insufficient eigenvectors
77(2)
4.5.5 General defective matrix
79(2)
5 Nonlinear Autonomous Interactions
81(36)
5.1 Predator-Prey Interaction
81(6)
5.1.1 Rabbits and foxes
81(1)
5.1.2 Reduction of order
82(3)
5.1.3 Critical points
85(1)
5.1.4 Linear stability analysis
86(1)
5.2 Linear Autonomous Systems
87(9)
5.2.1 Critical point and its stability
87(2)
5.2.2 Phase portrait
89(4)
5.2.3 Stability regions
93(3)
5.3 Nonlinear Autonomous Systems
96(7)
5.3.1 Critical points
96(1)
5.3.2 Linear stability analysis
97(3)
5.3.3 Hyperbolic critical points
100(3)
5.4 The Phase Portrait
103(7)
5.4.1 Limit cycles
103(3)
5.4.2 Non-existence of a limit cycle
106(1)
5.4.3 Reversible systems
107(2)
5.4.4 Multiple eigenvalues
109(1)
5.5 Basic Bifurcation Types
110(7)
5.5.1 The bacteria-antibody problem
110(2)
5.5.2 The three basic types of bifurcation
112(1)
5.5.3 Hopf bifurcation
113(4)
6 HIV Dynamics and Drug Treatments
117(20)
6.1 The Human Immunodeficiency Virus (HIV)
117(5)
6.1.1 HIV is a retrovirus
117(1)
6.1.2 The immune system
117(1)
6.1.3 The virus life cycle
118(1)
6.1.4 Three phases of HIV infection
119(1)
6.1.5 Treatment of HIV
120(1)
6.1.6 The principal direction of HIV research
121(1)
6.2 HIV Dynamics
122(8)
6.2.1 Model formulation
122(1)
6.2.2 Steady states and bifurcation for virus saturation
123(3)
6.2.3 Steady states and bifurcation for a small virus population
126(1)
6.2.4 The three-component model
127(3)
6.3 Drug Treatments
130(7)
6.3.1 The activities of HIV
130(1)
6.3.2 Combining RT and protease inhibitor
131(2)
6.3.3 Effectiveness of AIDS cocktail treatments
133(1)
6.3.4 On the modified three-component model
134(3)
7 Index Theory, Bistability and Feedback
137(22)
7.1 Poincare Index for Planar Systems
137(3)
7.2 Bistability - A Dimerized Reaction
140(3)
7.2.1 Interaction involving a dimer
140(1)
7.2.2 Fixed points and bifurcation
141(1)
7.2.3 Linear stability analysis
141(2)
7.3 Bistability - Two Competing Populations
143(8)
7.3.1 Leopards and hyenas
144(1)
7.3.2 Critical points
145(1)
7.3.3 Linear stability analysis
145(1)
7.3.4 Existence of bistability
146(2)
7.3.5 Other bistability configurations?
148(2)
7.3.6 Multiple bifurcation parameters
150(1)
7.4 Cell Lineages and Feedback
151(10)
7.4.1 Multistage cell lineages
151(2)
7.4.2 Performance objectives
153(1)
7.4.3 Feedback control of output
153(1)
7.4.4 A finite steady state
154(1)
7.4.5 Linear stability
155(1)
7.4.6 Fast regeneration time
156(3)
Part
3. Optimization		 159(70)
8 The Economics of Growth
161(10)
8.1 Maximum Sustained Yield
161(3)
8.1.1 Fishing effort and maximum sustainable yield
161(2)
8.1.2 Depensation and other growth rates
163(1)
8.2 Economic Overfishing vs. Biological Overfishing
164(4)
8.2.1 Revenue for a price taker
164(1)
8.2.2 Effort cost and net revenue
165(1)
8.2.3 Economic overfishing vs. biological overfishing
166(1)
8.2.4 Regulatory controls
166(2)
8.3 Discounting the Future
168(3)
8.3.1 Current loss and future payoff
168(1)
8.3.2 Interest and discount rate
169(2)
9 Optimization over a Planning Period
171(20)
9.1 Calculus of Variations
171(3)
9.1.1 Present value of total profit
171(1)
9.1.2 A problem in the calculus of variations
172(1)
9.1.3 The basic problem
173(1)
9.2 An Illustration of the Solution Process
174(3)
9.2.1 The action of a linear oscillator
174(1)
9.2.2 The condition of stationarity
175(1)
9.2.3 The Euler differential equation
176(1)
9.3 The General Basic Problem
177(3)
9.3.1 The fundamental lemma
177(2)
9.3.2 Euler differential equation for the basic problem
179(1)
9.4 Integration of Special Cases
180(4)
9.4.1 F(x,y,y') = F(x)
180(1)
9.4.2 F(x,y,y') = F(y)
180(1)
9.4.3 F(x,y,y') = F(y')
181(1)
9.4.4 F(x,y,y') = F(x,y')
182(1)
9.4.5 F(x,y,y') = F(y,y')
183(1)
9.4.6 F(x,y,y') = F(x,y)
183(1)
9.5 The Fishery Problem with Catch-Dependent Cost of Harvest
184(7)
9.5.1 The Euler DE and BVP
184(1)
9.5.2 Linear growth rate
184(1)
9.5.3 Constant unit harvest cost (c1 = 0)
185(2)
9.5.4 The method of most rapid approach
187(4)
10 Modifications of the Basic Problem
191(18)
10.1 Smooth and PWS Extremals
191(3)
10.2 Unspecified Terminal Unknown Value
194(5)
10.2.1 Euler boundary conditions
194(2)
10.2.2 Terminal payoff
196(3)
10.2.3 Euler boundary conditions with terminal payoff
199(1)
10.3 Higher Derivatives and More Unknowns
199(4)
10.3.1 Higher derivatives equivalent to more unknowns
199(1)
10.3.2 Euler differential equations for several unknowns
200(1)
10.3.3 Some examples
201(2)
10.4 Parametric Form and Free End Problems
203(6)
10.4.1 Basic problem in parametric form
203(1)
10.4.2 A first integral and Erdmann's conditions
204(1)
10.4.3 Free end problems
205(4)
11 Boundary Value Problems are More Complex
209(20)
11.1 Boundary Value Problems and Their Complications
209(2)
11.1.1 Second order equations
209(1)
11.1.2 No solution or too many solutions
210(1)
11.2 One-Dimensional Heat Conduction
211(7)
11.2.1 Rate of change of heat
211(2)
11.2.2 Fourier's law and the heat equation
213(1)
11.2.3 Steady state temperature distributions
214(2)
11.2.4 The time dependent problem
216(2)
11.3 Analytical Solutions for BVP
218(3)
11.3.1 Reduction of order for autonomous equations
218(2)
11.3.2 A nonautonomous nonlinear ODE
220(1)
11.4 The WP Approach for Linear BVP
221(4)
11.4.1 Homogeneous linear ODE
221(3)
11.4.2 Inhomogeneous ODE
224(1)
11.4.3 Some possible complications
225(1)
11.5 The Shooting Method
225(4)
Part
4. Constraints and Control		 229(96)
12 "Do Your Best" and the Maximum Principle
231(30)
12.1 The Variational Notation
231(3)
12.1.1 Variations of a function
231(1)
12.1.2 Variations of a function of functions
232(1)
12.1.3 Variations of the performance index
233(1)
12.2 Adjoint Functions
234(5)
12.2.1 A minimum cost problem
234(2)
12.2.2 Constraints on the investment rate
236(1)
12.2.3 The optimal control
237(2)
12.3 With Constraints, Do Your Best
239(4)
12.3.1 The augmented performance index
239(1)
12.3.2 The interior solution
240(1)
12.3.3 Do the best you can
241(2)
12.4 Fishery Problem without Prescribed Terminal Condition
243(5)
12.4.1 The "Do Your Best" approach
243(1)
12.4.2 Interior control is singular
244(1)
12.4.3 Upper corner solution near the end
245(1)
12.4.4 Optimal control for t < ts
246(2)
12.5 Optimal Allocation of Stem Cells for Medical Applications
248(1)
12.6 The Maximum Principle
249(12)
12.6.1 The Hamiltonian
249(1)
12.6.2 The general problem
250(1)
12.6.3 Maximization of the Hamiltonian
251(2)
12.6.4 The stem cell problem
253(2)
12.6.5 The fishery problem with constant unit harvest cost
255(4)
12.6.6 On the Maximum Principle
259(2)
13 Chlamydia Trachomatis
261(32)
13.1 A Proof of Concept Model of C. Trachomatis
261(5)
13.1.1 Life cycle of Chlamydia Trachomatis
261(1)
13.1.2 A linear growth rate model
261(2)
13.1.3 Hamiltonian and Maximum Principle
263(2)
13.1.4 Biological mechanisms for optimal strategy
265(1)
13.2 Chlamydia with Finite Carrying Capacity
266(6)
13.2.1 The model
266(2)
13.2.2 The singular solutions
268(1)
13.2.3 The upper corner control is optimal adjacent to T
269(2)
13.2.4 Lower corner control optimal only for R0 < or = to 1/2
271(1)
13.3 Optimal Conversion Strategy for Ro < or = to 1/2
272(8)
13.3.1 The optimal control is bang-bang for umax < 1/2
272(1)
13.3.2 Sub-interval of singular solution possible for umax > or = to 1/2
273(4)
13.3.3 On various threshold values
277(2)
13.3.4 Summary for R0 < or = to 1/2
279(1)
13.3.5 Case I - 0 < Ro < or = to Rc
280(1)
13.3.6 Case II - < Rc < R0 < 1/2
280(1)
13.4 Optimal Conversion Strategy for Ro > 1/2
280(8)
13.4.1 Upper corner control for 1 - umax > or = to Ro (> 1/2)
280(2)
13.4.2 Optimal conversion strategies for 1 - umax < Ro
282(3)
13.4.3 The relative magnitude of tx and ts
285(3)
13.4.4 Summary of the optimal conversion strategy for R0 > 1/2
288(1)
13.4.5 Case III - umax < or = to 1/2
288(1)
13.4.6 Case IV - umax > 1/2
288(1)
13.5 Mathematics and the Biology of Chlamydia
288(5)
14 Genetic Instability and Carcinogenesis
293(22)
14.1 Genetic Instability is a Two-Edge Sword
293(2)
14.2 Activation of an Oncogene
295(3)
14.2.1 A one-step system
295(1)
14.2.2 Dependence of death rate on mutation rate
296(1)
14.2.3 Dimensionless formulation
297(1)
14.3 Shortest Time by a Constant Mutation Rate
298(3)
14.3.1 An alternative description of the evolving populations
298(1)
14.3.2 Numerical solution for a time-invariant control
299(2)
14.4 The TOP
301(5)
14.4.1 Fastest time to cancer
301(1)
14.4.2 The Maximum Principle
302(2)
14.4.3 Some preliminary results on adjoint functions
304(2)
14.4.4 Vanishing Hamiltonian for our TOP
306(1)
14.5 Strictly Concave Death Rates
306(4)
14.5.1 Upper corner control near the start
306(2)
14.5.2 Optimal mutation rate is bang-bang
308(2)
14.5.3 General strictly concave death rate
310(1)
14.6 Optimal Switch Point for Bang-Bang Mutation
310(4)
14.6.1 A brute force scheme on xs= x2(Ts)
310(1)
14.6.2 Some bounds for the optimal switch time
311(3)
14.7 Other Types of Death Rates
314(1)
14.7.1 A death rate linear in mutation rate
314(1)
14.7.2 Strictly convex death rate
314(1)
15 Mathematical Modeling Revisited
315(10)
15.1 From Simple to Complex
315(3)
15.1.1 Simple question
315(1)
15.1.2 Simple model and upgrading
316(1)
15.1.3 Instantaneous rate of change
317(1)
15.2 Open to Options
318(3)
15.2.1 Higher order rates of change?
318(1)
15.2.2 Mathematical effectiveness & computational efficiency
319(2)
15.3 Improvement or Alternative
321(2)
15.3.1 Weighted parameter estimation
321(1)
15.3.2 Rate limiting carrying capacity
322(1)
15.4 Active Modeling Experience
323(2)
Appendix A First Order ODE 325(10)
A.1 Separable ODE
325(3)
A.1.1 Reduction to a calculus problem
325(1)
A.1.2 Initial condition and the initial value problem
326(1)
A.1.3 Scale invariant first order ODE
327(1)
A.2 First Order Linear ODE
328(2)
A.2.1 Integrating factor
328(1)
A.2.2 The Bernoulli equation
329(1)
A.3 An Exact First Order ODE
330(3)
A.3.1 Test for an exact equation
330(1)
A.3.2 Reduction to a calculus problem
331(2)
A.4 When an ODE Is Not Exact
333(1)
A.5 Summary of Methods for First Order ODE
334(1)
Appendix B Basic Numerical Methods 335(16)
B.1 Simple Euler
335(1)
B.2 Slowly
336(2)
B.3 But Not So Surely
338(3)
B.4 No Clue
341(2)
B.5 Clueless?
343(3)
B.6 Well-Posed Problems
346(2)
B.7 Higher Order Numerical Schemes for IVP
348(3)
Appendix C Assignments 351(18)
C.1 Assignment I
351(1)
C.2 Assignment II
352(2)
C.3 Assignment III
354(2)
C.4 Assignment IV
356(2)
C.5 Assignment V
358(1)
C.6 A Typical Midterm Examination
359(1)
C.7 Assignment VI
360(2)
C.8 Assignment VII
362(1)
C.9 Assignment VIII
363(2)
C.10 A Typical Final Examination
365(4)
Bibliography 369(2)
Index 371
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97898131433572e.html
Keywords: