nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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154 Additional Figures Figure B.22 A classical diagram of the imaginary part versus real part of the eigenvalues for the Jacobian evaluated in fixed points in the upper inflamed region (setting f2 = 1 × 10 −5 ).
B.6 Stable Spirals for f1 near the Bifurcation Point 155 B.6 Stable Spirals for f1 near the Bifurcation Point Here we present a series of phase space plots that show how the stable spiral behaves as f1 nears the bifurcation point. f1 grows from left to right in every figure and also as we go down through the figures. In figure B.25 f1 changes very little from the figure on the left to the right; f1 = 2.5663 × 10 −5 on the left, f1 = 2.566305 × 10 −5 on the right. We have made such minuscule changes because this is very close to the bifurcation point. For f1 = 2.574 × 10 −5 the spiral has vanished, and the phase space curve tends to the healthy rest state; cf. figure 8.4. The figures should be self-explanatory so we will not bother with a lot of repetitive caption. Figure B.23 Figure B.24
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- I, OM OG MED MATEMATIK OG FYSIK E
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Exploring Treatment Strategies for
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Preface iii questions that were out
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vi Contents Significance of the Apo
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List of Tables 5.1 summarizes the m
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x List of Figures 8.3 Phase space p
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xii
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2 Introduction In the following dec
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4 Introduction There are several sc
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6 Introduction because I had to mak
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8 Type 1 Diabetes and Its Etiology
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10 Type 1 Diabetes and Its Etiology
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3 Prospects for Therapy - A Mini Re
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3.3 Gastrin 15 eration in situ Urus
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4 Mathematical Modelling The langua
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5 The DuCa Model In the following w
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5.3 The DuCa Model - An Appetiser 2
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5.4 The DuCa Model - Compartment Mo
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5.6 Our Compartment Model 29 migrat
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5.6 Our Compartment Model 31 a ✓
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5.7 Discussion of Marée et al. (20
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5.7 Discussion of Marée et al. (20
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5.8 Discussion of Parameters 37 Fig
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5.8 Discussion of Parameters 39 Par
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5.8 Discussion of Parameters 41 tha
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5.8 Discussion of Parameters 43 Fig
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46 The Intermediated Model The diff
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48 The Intermediated Model expected
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50 The Intermediated Model Stabilit
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52 The Intermediated Model restrict
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54 The Intermediated Model We see t
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56 The Intermediated Model paramete
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58 The Intermediated Model ✻ Ma(t
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60 The Intermediated Model 6.2 The
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62 The Intermediated Model ✻ Ma(t
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7 A Brief Introduction to Bifurcati
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7.2 The Hopf bifurcation 67 the gen
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7.3 Biological Relevance of Bifurca
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7.5 Locating the Fixed Points 71 Ev
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74 Bifurcation Diagrams and Analysi
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98 Discussion of the Bifurcation An
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100 Discussion of the Bifurcation A
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102
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Page 140 and 141: 126 Bibliography Christen, U. and M
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Page 144 and 145: 130 Bibliography Yu, J. and G. S. E
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Page 172 and 173: 158 matlab Code w(r+1)=w(r)+dw; g=w
Page 174 and 175: 160 matlab Code end V_11(r)=E(1); V
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Page 178 and 179: 164 matlab Code M=M’; % end s_7(r
Page 180 and 181: 166 matlab Code w_7,V_34,’.b’,w
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Page 188 and 189: 174 Index value, 73 Bifurcation Ana
Page 190 and 191: 176 Index of diabetes, 2 Michaelis
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nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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