[Paper Review] Scaling property and opinion model for interevent time of terrorism attack

Jun-Fang Zhu, Xiao-Pu Han+1 more|ArXiv.org|Oct 21, 2009

Opinion Dynamics and Social Influence1 references3 citations

TL;DR

This paper proposes an opinion dynamics model with memory effects on a 2D lattice to explain the scale-free interevent time distribution of terrorism attacks in Iraq and Afghanistan (2003–2007). By incorporating social conformity and self-affirmation psychology, the model reproduces power-law interevent time distributions with exponents α = 2.43 (Iraq) and α = 2.35 (Afghanistan), matching empirical data and revealing individual psychological mechanisms as key drivers of collective violence bursts.

ABSTRACT

The interevent time of terrorism attack events is investigated by empirical data and model analysis. Empirical evidence shows it follows a scale-free property. In order to understand the dynamic mechanism of such statistic feature, an opinion dynamic model with memory effect is proposed on a two-dimension lattice network. The model mainly highlights the role of individual social conformity and self-affirmation psychology. An attack event occurs when the order parameter of the system reaches a critical value. Ultimately, the model reproduces the same statistical property as the empirical data and gives a good understanding of terrorism attack.

Motivation & Objective

• To investigate the statistical scaling properties of interevent times between terrorism attacks in Iraq and Afghanistan from 2003 to 2007.
• To understand the underlying dynamic mechanisms behind the observed power-law distribution of interevent times.
• To explore the role of individual psychological factors—social conformity and self-affirmation—in driving collective violence events.
• To develop a computational model that reproduces empirical interevent time distributions by simulating opinion formation with memory effects.
• To assess how social conformity, self-affirmation, and social chaos influence the emergence of terrorism events.

Proposed method

• An agent-based opinion dynamics model is constructed on a 2D lattice, where each agent holds an opinion value influenced by neighbors and personal memory.
• The model incorporates two psychological factors: social conformity (influence from neighbors) and self-affirmation (resistance to opinion change), controlled by parameters a and b.
• A memory effect is embedded via a time-dependent opinion update rule that retains historical opinion states, affecting current opinion evolution.
• The order parameter m, representing public consensus, is calculated as the average opinion across the lattice and evolves over time.
• A terrorism event is triggered when the order parameter m reaches a critical threshold mc, modeling the tipping point of collective action.
• The model is simulated over 100 independent runs with tuned parameters (a, b, T, mc) to match empirical interevent time distributions in Iraq and Afghanistan.

Experimental results

Research questions

• RQ1 Does the interevent time distribution of terrorism attacks in Iraq and Afghanistan follow a power-law or scale-free distribution?
• RQ2 What psychological mechanisms—specifically social conformity and self-affirmation—contribute to the observed scaling behavior in terrorism attack sequences?
• RQ3 How do memory effects in individual opinion dynamics influence the emergence and timing of collective violence events?
• RQ4 Can a model based on opinion dynamics with memory reproduce the empirical power-law interevent time distributions observed in real-world terrorism data?
• RQ5 What role does the critical threshold of public consensus (mc) play in determining the frequency and clustering of terrorism events?

Key findings

• The interevent time distribution of terrorism attacks in Iraq (2003–2007) follows a power law with a scaling exponent α = 2.43, and in Afghanistan, α = 2.35.
• The proposed opinion dynamics model with memory effects successfully reproduces the empirical power-law distribution of interevent times in both countries.
• Strong self-affirmation and weak social conformity are key psychological traits associated with the higher clustering of attacks in Iraq.
• In Afghanistan, self-affirmation and social conformity are more balanced, leading to a slightly lower scaling exponent compared to Iraq.
• The critical threshold mc for public consensus significantly influences event frequency: lower mc leads to more frequent attacks.
• The chaotic degree of social environment (T) affects the power exponent, with higher T increasing the likelihood of shorter interevent times.