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Research Methods: The Case for Nonlinear Dynamic Systems

Margaret Morison, MA

September 29, 2022

Nonlinear dynamic systems (NDS) is a general theory that describes and predicts changes over time (i.e., dynamics; Gregson & Guastello, 2011). Whereas a linear approach assumes that input is proportional to output, NDS allows us to model sudden changes, such as properly timed jumps from small inputs producing vast changes to a system. Although a substantial body of research has identified variables critical to understanding trauma exposure and its aftereffects—such as factors related to resilience or vulnerability—it often attempts to examine these dynamic constructs in a static, linear fashion. I will briefly discuss why the general linear approach may fall short and how NDS allows us to look at critical variables in ways that capture complex relationships.

Linearity is Not the Norm

Constructs such as thoughts, feelings, and behaviors may change discontinuously, sometimes appearing abrupt and tumultuous. As many clinicians readily observe, trauma survivors struggling to cope with their experience and the aftermath of that experience may not follow a linear upward trajectory towards normative functioning. Instead, attempts at recovery following trauma may follow a turbulent trajectory, with small successes and improvements in symptoms alternating with steps backward. We can see evidence of this nonlinear pattern in trajectory studies (see Galatzer-Levy et al., 2018 for review) and have some sense of what could be driving turbulence post-trauma (e.g., life stressors; Andersen et al., 2014; Bryant et al., 2015; Osenbach et al., 2014; Pietrzak et al., 2014), but we know little about how the process is unfolding. Statistical approaches that rest on the assumption of linearity may only take our understanding of the recovery process so far. As is often quoted in applied settings and among the lay public, "Healing is not linear."

The Nonlinear Alternative

Individuals are conceptualized as self-organizing living systems when employing an NDS framework to understand resilience and recovery. Self-organizing systems are composed of countless components that interact in complex ways (Pincus & Metten, 2010). Through reciprocal feedback loops between these components, the system is maintained over time. Consider the factors involved in one's vulnerability to posttraumatic stress disorder (PTSD). The potential factors impacting one's development and maintenance of PTSD span a wide range of areas, including historical (e.g., prior trauma; Ozer et al., 2003), psychological (e.g., low coping self-efficacy; Gallagher et al., 2020), social (e.g., insecure attachment; Woodhouse et al., 2015), and environmental (e.g., inaccessible/minimal resources; Unger, 2013) factors. Further, these individual components do not impact one's risk of PTSD in a silo. Instead, the complex relationships between these factors and how they influence one another over time impact risk.

Within this new framework, outcomes such as PTSD may be considered an emergent phenomenon arising from interacting system components (Goldstein, 1999). Rather than treating causal factors as "outside" of the system, we assume they are a part of the system itself and instead look at how each system component coordinates to produce emergent characteristics (Pincus & Metten, 2010). In this sense, the focus of our research questions moves from looking at relationships among variables to the processes that maintain the system's current state. Much like how our Gestalt colleagues understand perception (Koffka, 1935), the "whole" of PTSD is different than the sum of its "parts."

NDS similarly opens a new way of thinking about constructs such as resilience. When trauma survivors are conceptualized as self-organized living systems, we can use NDS techniques to look at the structure of that system. A key aspect of self-organizing systems is that, depending on the rigidity or flexibility of their structure, they either remain stable or change over time given different environmental demands (Pincus & Metten, 2010; Pincus et al., 2014; Pincus et al., 2019). A resilient system is thus able to adjust its structure relative to the demands of the environment. Pincus and colleagues (2019) applied orbital decomposition analysis to examine the structure of individuals' personality traits, which included coping behaviors, emotion regulation, ability to take others' perspectives, and so on. In this context, a "rigid" trait structure meant individuals had a narrow range of options for adapting to environmental demands. In contrast, a more "flexible" structure allowed for greater adaptation and thus, resilience. We may ask questions such as: Are they exceedingly rigid in their method of coping with their trauma, leaving them stuck? Or are they overly flexible, reaching for anything to avoid thinking about their trauma?

Connections to Theory

This alternative to traditional linear approaches is not new to psychological theory. Indeed, Masten's (2021) multisystem conceptualization of resilience pulls from a systems perspective. Individuals are considered living systems embedded within broader systems, such as communities or cultures. This broad theory of resilience acknowledges and attempts to integrate the wide range of factors operating on multiple levels and time scales (e.g., genes, social processes, neighborhoods) that interact to influence one's resiliency over time.

Bryan et al. (2020) utilized dynamical systems thinking to understand suicidality. They argue that individuals contemplating suicide attempt to maintain a low-risk state and regain balance, but provided with internal and environmental stressors, they are destabilized. This destabilization pushes them towards a new steady state characterized by a high risk of suicidal behavior. Critically, Bryan et al.'s (2020) theory expands on prior theories of suicide by accounting for both cyclical as well as sudden or discontinuous (i.e., "out of the blue") trajectories towards a high-risk state.

Self-Regulation Shift Theory (SRST; Benight et al., 2017) applies a similar dynamical systems approach. SRST conceptualizes trauma survivors as living systems that, through a self-evaluative process, attempt to maintain a steady state of adaptive functioning. However, should a survivor perceive their ability to cope as poor, they may hit a critical threshold that launches them into a chaotic state of functioning. Using cusp catastrophe modeling, Benight et al. found evidence to support this notion in motor vehicle accident survivors (Benight et al., 2017) and wildfire survivors (Benight et al., 2020). Cusp models outperformed linear models in understanding the mechanisms involved in nonlinear shifts in distress. Thus, NDS may provide an avenue for getting our analyses closer to our theory.

Considerations for Psychology

Rarely are the dynamic relationships between variables of interest captured in psychological studies due, in part, to measurement limitations. Indeed, we are often only capturing one snapshot of time rather than the process as it unfolds. We know our constructs of interest change over time, but how many measurements do we need to capture that change in a meaningful way? For example, we may observe that while functioning changes somewhat from day to day, meaningful shifts in one's pattern of symptoms occur every week. Taken a step further, this would mean assessing functioning at the usual one-month, three-month, and six-month follow-ups glances over potentially clinically relevant patterns of change. However, determining the density of measurement required to capture dynamic patterns requires rich time-series datasets that are few and far between within the field of psychology. Thus, researchers must carefully consider the timing and frequency of measurements when using NDS approaches. Ecological momentary assessment (EMA) and physiological measures (e.g., heart rate, respiration) are well-suited for many NDS analyses.

About the Author

Margaret Morison, MA, is a second-year clinical doctoral student at the University of Colorado Colorado Springs (UCCS). She works as a psychological trainee in the university counseling center and as a graduate research assistant with the Lyda Hill Institute for Human Resilience. Margaret's interests include understanding self-regulating mechanisms post-trauma, attachment and interpersonal dynamics, and recovery from sexual assault.

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