Applying linear systems analysis to dynamic behavior.
Linear systems math gives you a crystal ball for behavior that changes smoothly over time.
01Research in Context
What this study did
Rasing et al. (1992) wrote a how-to guide for using linear systems math on behavior data.
They showed how to plug response streams into difference and differential equations.
The paper also moved the math up to second-order forms to catch smoother, slower trends.
What they found
The authors proved you can treat behavior like an electrical signal.
With the right equations you can forecast future response rates from past ones.
Second-order forms let the model bend, matching real-world data that drifts over days.
How this fits with other research
Vyse (2004) took the same math and asked why behavior stays stable across time and places.
He used the linear-systems lens to explain traits through molar accounts and behavioral momentum.
Krispin (2026) stretched the idea further, mapping systems rules onto how whole cultures evolve.
All three papers share one message: math that tracks change over time belongs in behavior analysis.
Why it matters
If your client’s data show waves, drifts, or slow rebounds, try plotting the session-by-session trend.
A simple moving average or difference equation can reveal the system’s natural rhythm.
You gain an early-warning chart that tells you when an intervention is truly working.
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02At a glance
03Original abstract
In this paper we present an abbreviated discussion of the linear systems analysis in the time domain. We then consider the qualitative character of the behavioral dynamics predicted using the linear form of the analysis. The analysis is then extended to a second-order form. We illustrate some relevant new features introduced by the second-order form with a special case example.
Journal of the experimental analysis of behavior, 1992 · doi:10.1901/jeab.1992.57-377