dynamical system method
Definition
Dynamical system method is a mathematical framework for modeling a system's dynamic evolution, typically formulated in terms of linear or nonlinear ordinary differential equations on a state-space. In this framework, each group member's behavior is represented as a set of temporal relations in which behavior at the current time point is an outcome of that member's own prior behavior and the prior behavior of other group members. Social influence, whether assimilative or repulsive, can then be inferred from the direction of these temporal relations between each dyad. Applied to self-disclosure behavior across 18 therapy groups, the method enabled estimation of dyad-level social influence without imposing the assumption that all influence is uniform or assimilative, and it accommodated the simultaneous presence of both influence types within the same group.
Sources: Yang et al. (2024)
Related Terms
- group process (1 shared article)
- social influence (1 shared article)
- Boolean network (1 shared article)
- network control (1 shared article)
Applications
Dynamical System Method and Boolean Network Method
The Boolean network method is a specific implementation of dynamical system principles, modeling the evolution of group behavior from one discrete time point to the next using Boolean functions such as AND, OR, and NOT. Applied to longitudinal self-disclosure data from therapy groups, this approach retained the temporal-relational logic of dynamical systems while making the framework tractable for empirical behavioral data. The combination allowed both the inference of social influence patterns and the design of control strategies to direct groups toward desired behavioral states.
Sources: Yang et al. (2024)
Dynamical System Method and Social Influence
The dynamical system method estimates dyad-level social influence directly from behavioral time series, without assuming that influence is uniform across dyads. When a positive temporal relation exists between one person's behavior at time t and another's at t+1, assimilative influence is inferred; a negative temporal relation indicates repulsive influence. Across 18 therapy groups, 16 of the resulting Boolean network models included both assimilative and repulsive social influence simultaneously, a finding that prior modeling approaches were not designed to detect.
Sources: Yang et al. (2024)
Dynamical System Method and Group Management Strategies
Because the dynamical system method models behavior change as a group process governed by temporal interdependencies, it creates a foundation for applying control theory to identify network management strategies. In the therapy group application, this yielded group-specific strategies that could elicit self-disclosure from the majority of members without requiring manipulation of existing social ties. Useful control strategies were identified for 6 of the 18 groups, while 10 groups were already functioning in ways that made intervention unnecessary.
Sources: Yang et al. (2024)
