1. LINEAR AND NONLINEAR DYNAMICS IN INTIMATE PARTNER VIOLENCE
David Katerndahl, MD
Sandra Burge, PhD
Robert Ferrer, MD
Johanna Becho
Robert Wood, DrPH
Reuben McDaniel, EdD
Acknowledgment: This study was supported by a grant from the National Science Foundation.

2. CYCLIC THEORY OF VIOLENCE1.
Tension-Building
Phase 2.
Explosion! 3.
Calm, Loving
Respite

3. POWER AND CONTROL WHEEL
Violence
Using
Coercion
& Threats
Using
Intimidation
Using
Emotional
Abuse
Using
Economic
Control
Power
and
Control
Using Male
Privilege
Using
Isolation
Using
Children
Denying,
Blaming,
Minimizing
Violence

4. FAMILY SYSTEMS THEORY Wife Husband Interaction reaction action

5. SUMMARIZING DYNAMICS Degree Of Nonlinearity Dynamic Pattern Meaning
Output Not Proportional To Input
Unpredictability
Types
Information-Based
Algorithmic Complexity
Chaos-Based
Dynamic Pattern
Periodic Dynamics
Random Dynamics
Chaotic Dynamics

6. Framework For Understanding Dynamics
Periodic Dynamics

7. Framework For Understanding Dynamics
Random Dynamics

8. Framework For Understanding Dynamics
Chaotic Dynamics

9. FRAMEWORK FOR UNDERSTANDING DYNAMICS
Periodic, Predictable Recurrences
(Cyclic Theory) → Periodic Dynamics
Constant Stressors With Variable Violence
(Power Wheel Theory) → Random Dynamics
Variable Strength & Direction Of Feedback (Systems Theory) → Chaotic Dynamics

10. METHODS

11. Subject Protections No History Of Severe Violence
Community Resources Available
Hide Study Materials
Tell Partner About Involvement
-Not Study Topic
Coded Interactive Verbal Response
Weekly Contact At Safe Phone
Taken to FJC at End of Study

12. ANALYSIS Imputation Of Missing Data: TISEAN nstep procedure
Assessment Of Nonlinearity
Information-Based: Approximate Entropy
Algorithmic Complexity: LZ Complexity
Chaos-Based: Lyapunov Exponent
Identification Of Dynamic Patterns: Lyapunov vs CD Saturation
Identification Of Correlates Of Violence
Same-Day Correlates: Cross-Correlations
Prior-Day Correlates: Vector Autoregression Causality & Coefficients
Combination Of Measures Across Subjects
Cross-Correlations: Squaring rs (Glass, 1978)
p-Values: Z-statistics (Souffer et al, 1966)
Coefficients: Weighted By SEs (Greenland, 1987)

13. STUDY RESULTS 20 Women Enrolled Ethnicity: 80% Hispanic
Age: Years Old
Education: <7 Years – College Grad
Employment: 45% Full-Time
Income: $5-10,000 - $60-70,000

14. STUDY RESULTS Household Environment
Husband’s Alcohol Intake - 75% Husbands ≥9 Drinks Daily
Hassles - Mean (0-30)
Stress % Days “Extremely Stressful”
Arguments % Days With Arguments
Closeness % Days Felt “Very Distant”

15. STUDY RESULTS Violence Reported Violence Reported - 225/586 (38%) Days
Frequent Violence
Threats Days
Throwing Things Days
Pushed/Slapped Days
Severe Violence
Kicked/Hit Women, 21 Days
Beaten Women, 5 Days
Weapons Woman, 31 Days

16. Patterns (Example) Constant Alcohol Intake
VIOLENCE
Constant Alcohol Intake
Same-Day Violence Relationships
Inverse - Closeness
Positive
Arguments
Stress
Period Of Sustained Violence
Hassles

17. POTENTIAL MANAGEMENT IMPLICATIONS
Nonlinearity
Treatment Response Unpredictable
Dynamics-Specific Approaches
Periodic – Simple Interventions
Chaotic – Control / Anti-Control
Random – Multifaceted Interventions
Daily Diaries – Avoid Violence
Triggers
Prior-Day Correlates

18. POTENTIAL RESEARCH IMPLICATIONS
Each Situation Unique
NO ONE THEORY CORRECT
Current Theories Only Part Of Whole
Transitions Between Theories
PERIODIC RANDOM CHAOTIC
CYCLIC POWER SYSTEMS
WHEEL