A Tutorial on Ordinary Differential Equations in Behavioral Science: What Does Physics Teach Us?

The present tutorial proposes to use concepts of physics and mathematics to help behavioral scientists to use differential equations in their studies. It focuses on the first-order and the second-order (damped oscillator) differential equation. Simple examples allow to detail the meaning of the coefficients, the conditions of applicability of these differential equations, the underlying hypothesis, and their consequences for the researcher willing to use them. More complex psychological examples demonstrate the importance of parameters' interpretation. Particular attention is paid to how potential external perturbations should be considered. The last decades have seen an increased interest in the use of differential equations to model longitudinal changes in behavioral science. Numerous statistical methods have been developed to estimate the coefficients of first- and second-order differential equations, with the goal of modeling the dynamics of return to equilibrium in a wide range of behavioral fields. The present tutorial proposes to use concepts of physics and mathematics to help behavioral scientists to avoid common pitfalls and misconceptions when using differential equations. It focuses on the first-order and the second-order (damped oscillator) differential equations. Simple examples allow to detail the meaning of the coefficients, the conditions of applicability of these differential equations, the underlying hypothesis, and their consequences for the researcher willing to use them. More complex psychological examples demonstrate the importance of parameters' interpretation. Particular attention is paid to how potential external perturbations should be considered. [ABSTRACT FROM AUTHOR]