What question did this study set out to answer?

To derive a five-variable extension of the Learning System Stability Model (LSSM).

March 15, 2026Open Access

A Five-Variable Coupled Dynamical Extension of the Learning System Stability Model

Key Points

To derive a five-variable extension of the Learning System Stability Model (LSSM).
Developed a coupled continuous-time dynamical system with five variables
Incorporated structural corrections including mass conservation and logistic growth
Provided Python implementation for practical application.
The model exhibits bistability consistent with original LSSM
Maintains stability constraint as a condition
Demonstrated dynamics of relevance in cognitive systems.

Abstract

This paper derives a five-variable coupled continuous-time dynamical extension of the Learning System Stability Model (LSSM). The system tracks labile traces (T), prior knowledge (E), relevance (r), synaptic consolidation (Sₛyn), and systems consolidation (Sₛys). Eight structural corrections are incorporated, including mass conservation, logistic knowledge growth bounded by capacity ceiling Eₘax, normalised selection function sigma in 0, 1, and saturated relevance dynamics. The corrected system is well-posed, admits bistability consistent with the original LSSM saddle-node structure, and preserves the stability constraint L ≤ E·Sₛys² as a slow-timescale condition. Reference Python implementation provided separately.

A Five-Variable Coupled Dynamical Extension of the Learning System Stability Model

Key Points

Abstract

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