The Mathematics of Marriage: Dynamic Nonlinear Models

Contents......Page 8
Preface......Page 12
1 What Do We Mean by Theory?......Page 20
2 What Phenomena of Marriage Are We Modeling?......Page 24
2.1 Brief Review of Research on Marriage The Scientific Study of Marriage......Page 25
2.2 The Problem of Power......Page 47
2.3 Review of Gottman and Levenson......Page 48
2.5 Two Additional Mysteries in the Marital Research Area......Page 53
3.1 The General Systems Theory of von Bertalanffy......Page 54
3.2 Modeling with More Than One Equation......Page 55
3.3 Outline of the Subsequent Chapters......Page 57
4 Calculus—the Mathematics of Change......Page 60
4.1 Dynamical Motion as Slope......Page 61
4.2 The Concept of a Function......Page 64
4.3 Limits......Page 70
4.4 The Derivative Is a Limit......Page 71
4.5 Common Derivatives in Functional Form......Page 72
4.6 Rules for Differentiation......Page 73
4.8 Maxima and Minima......Page 75
4.9 Problem......Page 77
4.10 Writing Differential Equations......Page 78
4.11 Taylor\'s series......Page 80
5.1 Philosophy of Modeling......Page 84
5.2 A Bit of Dynamical Modeling History......Page 87
5.3 One Equation: Malthus Revisited......Page 88
Appendix 5.1: Stability Results......Page 98
6 Modeling Catastrophic Change......Page 100
6.1 The Spruce Budworm Problem......Page 101
6.2 Courtship, Marriage, Divorce, and the Spruce Budworm Catastrophe......Page 107
6.3 Examples of Catastrophic Change: Christopher Zeeman......Page 108
6.4 Catastrophes in Perception......Page 112
6.5 Chapter Summary......Page 116
Appendix 6.1: Nondimensionalization......Page 117
7.1 Phase Space Portrait......Page 118
7.2 Force Field Portrait......Page 119
7.3 Null Clines and Steady States......Page 120
Appendix 7.1: Phase Plane Analysis......Page 123
8.1 A Linear Marriage Model: Romeo and Juliet\'s Love Affair......Page 130
8.2 Predator and Prey Models (the Lotka-Volterra Equations)......Page 132
8.3 Competition Models......Page 138
8.5 Chapter Summary......Page 141
Appendix 8.1: Nonlinear Modeling Concepts Nondimensionalizing the Lotka-Volterra Equations......Page 143
9 Writing the Equations of Marriage......Page 146
9.1 The Model......Page 148
9.2 Estimating of Parameters and Fitting the Influence Functions......Page 153
9.3 Finding the Null Clines and the Influenced SetPoints......Page 154
9.4 Steady States and Stability......Page 156
9.5 The Marriage Model and Catastrophes......Page 160
Appendix 9.1: The Inertia Parameter......Page 163
Appendix 9.2: Stability of the Steady States(Marriage Model)......Page 164
Appendix 9.3: Measuring the Strength of Attraction of a Stable Steady States......Page 168
10.1 Power and Affect: Influence Functions......Page 170
10.2 Mismatch Theory: The Possibility That Unstable Marriages Are the Results of Failed Attempts at Creating a Pure Type......Page 173
10.3 Set Points and Inertia......Page 175
10.4 Validation of the Model Parameters......Page 176
10.5 Discussion of Initial Modeling Results......Page 179
10.6 Prospects for Extending the Model......Page 181
11.1 Homeostasis and Feedback......Page 184
11.2 Family Dynamics......Page 188
11.3 Disconfirmability......Page 189
11.5 The Conceptual Power of the Mathematical Model: A New General Systems Language of Marriage......Page 190
12.1 Developing the SPAFF Coding System......Page 192
12.2 Fitting an Ojive Model to Weighted SPAFF Data......Page 194
12.3 Seattle Newlywed Study......Page 196
12.4 Initial Weighting for the SPAFF......Page 200
12.5 Final Weighting Scheme for the SPAFF......Page 202
12.6 Understanding the Uninfluenced Steady States......Page 205
12.7 Chapter Summary......Page 206
13.1 What Are Repair and Damping?......Page 208
13.2 The Repair and Damping Terms......Page 211
13.3 The Bilinear and Ojive Influence Functions......Page 217
13.4 Simulations regarding Repair and Damping......Page 223
13.5 Methods for Evaluating the Two Alternatives......Page 229
13.6 Results......Page 230
13.7 Model Behavior with Repair and Damping Null Clines and Steady States......Page 238
13.8 Interpretations and Predictions......Page 250
14.1 Gay Male and Lesbian Relationships......Page 252
14.2 Parent-Baby Interaction: Extending the Marriage Model to Triads......Page 260
14.3 Chapter summary......Page 269
15.1 What Is the Core Triad of Balance?......Page 270
15.2 On What Data Do We Base the Model?......Page 271
15.3 Brief Review of Behavior-Based Models......Page 276
15.4 Core Triad Model Specification......Page 277
15.5 Core Triad Model Results......Page 279
15.6 Chapter Summary......Page 308
16 The Marriage Experiments......Page 310
16.1 Evaluation of Couples Therapy......Page 312
16.2 Gottman\'s New Theory and Marital Intervention......Page 316
16.3 The Three Goals of an Empirically Based Marital Intervention and Rationale for the Marriage Experiments......Page 321
16.4 The Dreams-Within-Conflict Intervention: An In-Depth Look......Page 329
16.5 Angie and Dave: Overview The State of the Marriage......Page 332
16.6 Angie and Dave: The Dreams-within-Conflict Intervention......Page 336
16.7 Angie and Dave: Second Conversation......Page 342
16.8 Angie and Dave: Math Model......Page 350
16.9 Alan and Eve......Page 352
16.10 Chapter Summary......Page 354
17.1 Obtaining the Model Program......Page 356
17.2 Basic Concepts in Data Preparation......Page 357
17.3 Example: Deriving Model Data from SPAFF......Page 358
Bibliography......Page 362
Appendix A: Model Analysis......Page 380
Appendix B: More Complex Repair and Damping......Page 384
B.1: Repair Determined by Own Slope and Own Score......Page 385
B.2: Repair Determined by Spouse\'s Slope and OwnScore......Page 395
B.3: Repair Determined by Own Slope and Spouse\'s Score......Page 400
B.4: Repair Determined by Spouse\'s Slope and Spouse\'s Score......Page 410
Index......Page 416