Modeling Love Dynamics

by Sergio Rinaldi, Fabio Della Rossa, Fabio Dercole, Alessandra Gragnani, Pietro Landi

Overview

This book shows, for the very first time, how love stories — a vital issue in our lives — can be tentatively described with classical mathematics. Focus is on the derivation and analysis of reliable models that allow one to formally describe the expected evolution of love affairs from the initial state of indifference to the final romantic regime. The models are in full agreement with the basic philosophical principles of love psychology. Eight chapters are theoretically oriented and discuss the romantic relationships between important classes of individuals identified by particular psychological traits. The remaining chapters are devoted to case studies described in classical poems or in worldwide famous films.

Product Details

ISBN-13:	9789813224414
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	12/14/2015
Series:	World Scientific Series On Nonlinear Science Series A , #89
Pages:	256
Product dimensions:	6.00(w) x 9.00(h) x 0.54(d)

Table of Contents

Preface v

1 Can we model love stories? 1

1.1 Graphical representation of love stories 2

1.2 The models 5

1.3 ODE models 7

1.4 Individual chaxacteristies: Oblivion, reaction to appeal, and reaction to love 9

1.5 From individuals to couples 13

1.6 Summary of results 14

Simple models 17

2 Linear models and then properties 19

2.1 Historical premise 20

2.2 Five properties of the model 24

2.3 Consequences at community level 28

3 Couples composed of secure and unbiased individuals 33

3.1 The model 34

3.2 Alternative stable states 35

3.3 Bifurcation analysis 37

3.4 Temporary bluffing in love affairs 40

4 Roxane and Cyrano 43

Modeling Love Dynamics

4.1 The story of Roxane and Cyrano 44

4.2 The model of Roxane and Cyrano 46

4.3 Model validation 50

4.4 Conclusions 53

5 The discovery of hidden components of the appeal 55

5.1 Catastrophic bifurcations 55

5.2 Beauty and The Beast 57

5.3 Elizabeth and Darcy 60

5.4 Conclusions 64

6 Couples composed of insecure and unbiased individuals 65

6.1 The model 66

6.2 The case of identical individuals 68

6.3 The general case 71

6.4 Conclusions 74

7 Scarlett and Rhett 75

7.1 The love story between Scarlett and Rhett 76

7.2 The model 80

7.3 Validation of the model 82

7.4 Conclusions 84

8 Romantic cycles 87

8.1 Introduction 88

8.2 No bias implies no cycles 88

8.3 No insecurity implies no cycles 89

8.4 A first example of romantic cycle 91

8.5 A second example of romantic cycle 96

9 Kathe and Jules 99

9.3 The story 100

9.2 The Kathe-Jules model 101

9.3 Analysis and results 104

10 Kathe and Jim 111

10.1 The Kathe-Jim model 112

10.2 Analysis and results 114

Complex models 119

11 Environmental stress and romantic chaos 121

11.1 Do couples replicate environmental stresses? 122

11.2 Canonical responses to stress 125

11.3 Romantic chaos 129

11.4 An example of romantic chaos 131

12 Extra emotional dimensions 141

12.1 Introduction 141

12.2 The model 143

12.3 Analysis and results 144

12.4 Slow-fast dynamics 147

13 Laura and Francesco 149

13.1 Petrarch's romantic cycle 150

13.2 A model of Laura and Francesco 153

13.3 Calibration of the model 155

13.4 The L-F cycle and its validation 157

13.5 Reliability of the results and discussion 159

13.6 The great conjecture 161

14 Triangular love stories and unpredictability 163

14.1 Triangular relationships 164

14.2 A catalog of triangles 166

14.3 Jealousy, conflict, and unpredictability 169

14.4 Conclusions and discussion 174

15 Kathe, Jules, and Jim 177

15.1 The story 178

15.2 The free-love hypothesis 179

15.3 The Kathe-Jules-Jim model 182

15.4 Analysis and results 184

15.5 The genius of Truffaut 188

Appendix A Appendix 191

A.1 A simple illustrative example 191

A.2 Dynamical systems and state portraits 196

A.3 Structural stability 205

A.4 Bifurcations as collisions 207

A.5 Local bifurcations 210

A.6 Global bifurcations 218

A.7 Catastrophes, hysteresis, and cusp 221

A.8 Routes to chaos 223

A.9 Numerical methods and software packages 225

Bibliography 231

Index 239