Modeling resilience with differential equations.

Abstract

A concept that has been bouncing around the psychological literature for some time is that of resilience, the idea that individuals can exhibit positive adaptation in the process of experiencing adverse life events. Simply put, one might say resilient people bounce back from negative events. The New Shorter Oxford English Dictionary (1993) contains the following definitions of resilience:1 a The action or act of rebounding or springing back. b Recoil from something; revolt. 2 Elasticity; spec. the amount of energy per unit volume that a material absorbs when subjected to strain. 3 The ability to recover readily from, or resist being affected by, a setback, illness, etc. (p. 2562) These definitions constitute an interesting overlap of physical and psychological meanings. This overlap creates an intentional metaphor of elasticity when used to describe a short-term, intraindividual psychological process. However, positive adaptation and elasticity may have subtly differing meanings.In this chapter, we examine some models that can describe two physical properties, elasticity and damping, that are used to describe resilient physical systems. We propose that models such as these are important to consider if one wishes to make a claim of construct validity for the overlap between the physical and psychological meanings of resilience. In other words, our argument is that if we wish to measure how someone "bounces back," we need models that can parameterize the bounce. If we fit models describing components of physical elasticity to intraindividual psychological adaptation in the presence of stress and find that parts of the model do not provide explanatory power, then we would like to know what parts of the physical elasticity metaphor for resilience should be modified or discarded. Finally, by taking the physical elasticity metaphor seriously, we introduce a language for expressing differences between models that can help clarify our thinking about different forms of intraindividual adaptation to stress.

Risk Perception and the Economic Crisis: A Longitudinal Study of the Trajectory of Perceived Risk

“…A number of researchers have adopted this perspective and have investigated people's ability to regulate emotions like fear, anger, and sadness. ( 21‐23 ) Similar to Solomon, ( 18 ) they have noted that heightened emotions tend to oscillate about a personal baseline and dampen over time. Similarly, people differ in their emotional reactivity, and their ability to regulate these fluctuations.…”

“…Some researchers have proposed that the rate of decline in negative emotions may be proportional to the gap between current and baseline levels. ( 23 ) Because our study began when negative emotions were high, this gap was most likely large. As respondents adapted to the crisis, this discrepancy should shrink (according to the theory) and thus slow the rate of decline in negative emotions (and, by association, perceived risk).…”

Dynamics of Change and Change in Dynamics

“…As an example, psychological resilience is often described as the ability to “bounce back” from adversity. Hooke’s Law shows us that a simple model for elasticity with dissipation (akin to a bouncing ball that eventually comes to rest) is a linear second order differential equation (see Boker, Montpetit, Hunter, & Bergeman, 2010, for an extended discussion).…”

Adaptive equilibria: A balancing act of regulation in development

“…Momentum (Iso-Ahola & Mobily, 1980), spring and mass systems (Turvey, 1990), pendulums (Boker & Laurenceau, 2007; Reed, Barnard, & Butler, in press), thermostats (Chow, Ram, Boker, Fujita, & Clore, 2005), reservoirs (Deboeck & Bergeman, 2013) and elasticity (Boker, Montpetit, Hunter, & Bergeman, 2010) have been explored and sometimes empirically tested as models for processes that evolve over short (i.e., seconds), medium (i.e., days), or long (i.e., years) intervals of time. The appeal of these metaphors is that they can literally be embodied in order to provide a seed of understanding.…”

“…This framework accounts for short term regulation as a separate process from longer term adaptation. This separation of regulation into models at two different timescales is useful since we can then map it to a wide range of phenomena such as perceptual learning and its underlying neural mechanisms (Schiltz et al, 1999), acquired tolerance and withdrawl symptoms in substance dependence (Tiffany, 1990), the honeymoon effect in romantic relationships (Aron, Norman, Aron, McKenna, & Heyman, 2000), or resiliency in daily positive affect (Boker, Montpetit, et al, 2010). The adaptive equilibrium regulation framework can be used to model the macro behavior of basic neural mechansims and as such is likely to be useful for the analysis of many systems that regulate sensitivity, expressivity, and activity in living organisms.…”