Dynamic Regulation Responding to an External Stimulus: A Differential Equation Model

References

• Amazeen, P.G., Amazeen, E. L., & Turvey, M. T. (1998). Breaking the Reflectional Symmetry of Interlimb Coordination Dynamics. Journal of Motor Behavior, 30, 199–216, doi:10.1080/00222899809601337
   PubMed Web of Science ®Google Scholar
• Bisconti, T. L., Bergeman, C. S., & Boker, S. M. (2004). Emotional well-being in recently bereaved widows: A dynamical systems approach. The Journals of Gerontology: Series B, 59, P158–P167. doi:10.1093/geronb/59.4.P158
   Google Scholar
• Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2009). Statistical methods for modeling human dynamics: An interdisciplinary dialogue. In S. Chow, E. Ferrer, & F. Hsieh (Eds.), Generalized local linear approximation of derivatives from time series (pp. 161–178). Mahwah, NJ: Lawrence Erlbaum Associates. doi:10.4324/9780203864746
   Google Scholar
• Boker, S. M., & Graham, J. (1998). A dynamical systems analysis of adolescent substance abuse. Multivariate Behavioral Research, 33, 479–507. doi:10.1207/s15327906mbr3304_3
   PubMed Web of Science ®Google Scholar
• Boker, S. M., Neale, M. C., & Rausch, J. R. (2004). Latent differential equation modeling with multivariate multi-occasion indicators. In K. V. Montfort, J. Oud, & A. Satorra (Eds.), Recent developments on structural equation models: Theory and applications (pp. 151–174). Amsterdam: Kluwer. doi: 10.1007/978-1-4020-1958-6
   Google Scholar
• Boker, S. M., & Nesselroade, J. R. (2002). A method for modeling the intrinsic dynamics of intraindividual variability: Recovering the parameters of simulated oscillators in multi-wave panel data. Multivariate Behavioral Research, 37(1), 127–160. doi: 10.1207/S15327906MBR3701_06
   PubMed Web of Science ®Google Scholar
• Boyce, W. E., & DiPrima, R. C. (2012). Elementary differential equations and boundary value problems (10th ed.). New York, London, Sydney: John Wiley & Sons, Inc. doi: 10.2307/2314317
   Google Scholar
• Butner, J., Amazeen, P. G., & Mulvey, G. M. (2005). Multilevel modeling of two cyclical processes: Extending differential structural equation modeling to nonlinear coupled systems. Psychological Methods, 10(2), 159–177. doi:10.1037/1082-989X.10.2.159
   PubMed Web of Science ®Google Scholar
• Carver, C. S., & Scheier, M. F. (1998). On the self-regulation of behavior. Cambridge, New York: Cambridge University Press. https://doi.org/10.1017/CBO9781139174794
   Google Scholar
• Chow, S.-M., Ram, N., Boker, S. M., Fujita, F., & Clore, G. (2005). Emotion as a thermostat: Representing emotion regulation using a damped oscillator model. Emotion, 5(2), 208–225. doi: 10.1037/1528-3542.5.2.208
   PubMed Web of Science ®Google Scholar
• Deboeck, P. R. (2010). Estimating dynamical systems: Derivative estimation hints from Sir Ronald A. Fisher. Multivariate Behavioral Research, 45(4), 725–745. doi:10.1080/00273171.2010.498294
   PubMed Web of Science ®Google Scholar
• Deboeck, P. R., & Bergeman, C. S. (2013). The reservoir model: A differential equation model of psychological regulation. Psychological Methods, 18(2), 237–256. doi: 10.1037/a0031603
   PubMed Web of Science ®Google Scholar
• Deboeck, P. R., Boker, S. M., & Bergeman, C. S. (2008). Modeling individual damped linear oscillator processes with differential equations: Using surrogate data analysis to estimate the smoothing parameter. Multivariate Behavioral Research, 43(4), 497–523. doi:10.1080/00273170802490616
   PubMed Web of Science ®Google Scholar
• Driver, C. C., Oud, J. H. L., & Voelkle, M. C. (2017). Continuous time structural equation modelling with R package ctsem. Journal of Statistical Software, 77(5), 1–35. doi:10.18637/jss.v077.i05
   Web of Science ®Google Scholar
• Fitzpatrick, P., Schmidt, R. C., & Carello, C. (1996). Dynamical patterns in clapping behavior. Journal of Experimental Psychology: Human Perception and Performance, 22(3), 707–724. doi:10.1037/0096-1523.22.3.707
   Web of Science ®Google Scholar
• Fuchs, A., & Kelso, J. A. S. (1994). A theoretical note on models of interlimb coordination. Journal of Experimental Psychology: Human Perception and Performance, 20(5), 1088–1097. doi:10.1007/BF00336922
   PubMed Web of Science ®Google Scholar
• Gasimova, F., Robitzsch, A., Wilhelm, O., Boker, S. M., Hu, Y., & Hülür, G. (2014). Dynamical systems analysis applied to working memory data. Frontiers in Psychology, 5, 687. doi:10.3389/fpsyg.2014.00687
   PubMed Web of Science ®Google Scholar
• Gernigon, C., Vallacher, R. R., Nowak, A., & Conroy, D. E. (2015). Rethinking approach and avoidance in achievement contexts: The perspective of dynamical systems. Review of General Psychology, 19(4), 443–457. doi:10.1037/gpr0000055
   Web of Science ®Google Scholar
• Greenleaf, E. A. (1995). The impact of reference price effects on the profitability of price promotions. Marketing Science, 14(1), 82–104. doi:10.1287/mksc.14.1.82
   Web of Science ®Google Scholar
• Hamalainen, R. P., Luoma, J., & Saarinen, E. (2014). Mathematical modeling is more than fitting equations. American Psychologist, 69, 633–634. doi:10.1037/a0037048
   PubMed Web of Science ®Google Scholar
• Helm, J. L., Sbarra, D., & Ferrer, E. (2012). Assessing cross-partner associations in physiological responses via coupled oscillator models. Emotion, 12(4), 748–762. doi:10.1037/a0025036
   PubMed Web of Science ®Google Scholar
• Hoeksma, J. B., Oosterlaan, J., Schipper, E., & Koot, H. (2007). Finding the attractor of anger: Bridging the gap between dynamic concepts and empirical data. Emotion, 7(3), 638–648. doi:10.1037/1528-3542.7.3.638
   PubMed Web of Science ®Google Scholar
• Hu, Y., Boker, S. M., Neale, M. C., & Klump, K. (2014). Coupled Latent differential equations with moderators: Simulation and application. Psychological Methods, 19(1), 56–71. doi:10.1037/a0032476
   PubMed Web of Science ®Google Scholar
• Hubbard, J. H., & West, B. H. (1991). Differential equations: A dynamical systems approach. New York, NY: Springer.
   Google Scholar
• Kay, B. A., Kelso, J. A. S., Saltzman, E. L., & Schoner, G. (1987). Space-time behavior of single and bimanual rhythmical movements: Data and limit cycle model. Journal of Experimental Psychology: Human Perception and Performance, 13(2), 178–192. doi:10.1037//0096-1523.13.2.178
   PubMed Web of Science ®Google Scholar
• Montpetit, M. A., Bergeman, C. S., Boker, S. M., Deboeck, P. R., & Tiberio, S. S. (2010). Resilience-as-process: Negative affect, stress, and coupled dynamical systems. Psychology and Aging, 25(3), 631–640. doi:10.1037/a0019268
   PubMed Web of Science ®Google Scholar
• Moshinsky, M. (1969). The harmonic oscillator in modern physics: From atoms to quarks. New York, NY: Gordon & Breach.
   Google Scholar
• Nicholson, J. S., Deboeck, P. R., Farris, J. R., Boker, S. M., & Borkowski, J. G. (2011). Maternal depressive symptomatology and child behavior: Transactional relationship with simultaneous bidirectional coupling. Developmental Psychology, 47(5), 1312–1323. doi:10.1037/a0023912
   PubMed Web of Science ®Google Scholar
• Nijs, V. R., Dekimpe, M. G., Steenkamps, J.-B. E., & Hanssens, D. M. (2001). The category-demand effects of price promotions. Marketing Science, 20(1), 1–22. https://doi.org/10.1287/mksc.20.1.1.10197
   Web of Science ®Google Scholar
• Ostry, D., Keller, E., & Parush, A. (1983). Similarities in the control of the speech articulators and the limbs: Kinematics of tongue dorsum movement in speech. Journal of Experimental Psychology: Human Perception and Performance, 9(4), 622–636. http://dx.doi.org/10.1037/0096-1523.9.4.622
   PubMed Web of Science ®Google Scholar
• R Development Core Team. (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Reed, R. G., Barnard, K., & Butler, E. A. (2015). Distinguishing emotional coregulation from codysregulation: An investigation of emotional dynamics and body weight in romantic couples. Emotion, 15(1), 45–60. doi:10.1037/a0038561
   PubMed Web of Science ®Google Scholar
• Smith, L. B., & Thelen, E. (2003). Development as a dynamic system. Trends in Cognitive Sciences, 7(8), 343–348. http://dx.doi.org/10.1016/S1364-6613(03)00156-6
   PubMed Web of Science ®Google Scholar
• Soetaert, K., Petzoldt, T., & Setzer, R. W. (2010). Solving Differential Equations in R: Package deSolve. Journal of Statistical Software, 33(9), 1–25. doi:10.18637/jss.v033.i09
   PubMed Web of Science ®Google Scholar
• Steele, J. S., Ferrer, E., & Nesselroade, J. R. (2014). An idiographic approach to estimating models of dyadic interactions with differential equations. Psychometrika, 79, 675–700. doi:10.1007/s11336-013-9366-9
   PubMed Web of Science ®Google Scholar
• Sterman, J. D. (2002). All models are wrong: Reflections on becoming a systems scientist. System Dynamics Review, 18(4), 501–531. doi:10.1002/sdr.261
   Web of Science ®Google Scholar
• Voelkle, M. C., & Oud, J. H. (2013). Continuous time modeling with individual varying time intervals for oscillating and non-oscillating processes. British Journal of Mathematical and Statistical Psychology, 66(1), 103–126. doi:10.1111/j.2044-8317.2012.02043.x
   PubMed Web of Science ®Google Scholar
• von Oertzen, T., & Boker, S. M. (2010). Time delay embedding increases estimation precision of models of intraindividual variability. Psychometrika, 75(1), 158–175. doi:10.1007/S11336-009-9137-9
   PubMed Web of Science ®Google Scholar
• Wilson, T. D., Gilbert, D. T., & Centerbar, D. B. (2003). Making sense: The causes of emotional evanescence. In I. Brocas & J. D. Carillo (Eds.), The psychology of economic decisions (vol. 1: Rationality and well-being, pp. 209–233). New York, NY: Oxford University Press. doi:10.1016/j.socec.2003.10.007
   Google Scholar
• Wood, S. L., & Bettman, J. R. (2007). Predicting happiness: How normative feeling rules influence (and even reverse) durability bias. Journal of Consumer Psychology, 17(3), 188–201. doi:10.1016/S1057-7408(07)70028-1
   Web of Science ®Google Scholar