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Introduction Introduction
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Dynamical Systems: The Concept Dynamical Systems: The Concept
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The Language of Dynamical Systems The Language of Dynamical Systems
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Attractors and Self-Regulation Attractors and Self-Regulation
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Discrete and Continuous Time Discrete and Continuous Time
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First-Order Differential Equation Model First-Order Differential Equation Model
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Second-Order Differential Equation Model Second-Order Differential Equation Model
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Conclusions & Future Directions Conclusions & Future Directions
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Appendix A: Approximate Discrete Model Appendix A: Approximate Discrete Model
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Appendix B: Latent Differential Equation Modeling Appendix B: Latent Differential Equation Modeling
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Author Note Author Note
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Notes Notes
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References References
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19 Dynamical Systems and Models of Continuous Time
Get accessPascal R. Deboeck, Department of Psychology, University of Kansas, Lawrence, KS
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Published:01 October 2013
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Abstract
Historically it has been easier to focus on measuring and describing differences between groups of people rather than try to describe the dynamic ways that individuals change. Dynamical systems are mathematical models that aim to describe how constructs change over time. Frequently these models are continuous time models; models that try to capture the function that underlies a set of observations. This chapter introduces the concept of a dynamical system and of continuous time models. Two methods are introduced for the fitting of continuous time models to observed data: one using the approximate discrete model for a first-order autoregressive model and the second using a method of estimating latent derivatives for a second-order autoregressive model.
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