MesoNet: Lyapunov and linearization study

linearization + Lyapunov reading. remember the jumps at spike events, not only the nice continuous bit between them

study bundle: eigenvalues, Jacobians and Lyapunov functions as tools for connecting the proposed learning rule to stability. Keep local linearization and a global stability argument separate.

practical link: compare candidate stability quantities with firing-rate and weight histories already being logged. The source does not provide a complete verified Lyapunov proof in this entry; retain this as a mathematical work area rather than a theorem announcement.

Lyapunov heatmap

Bifurcation and Lyapunov notes

References saved in this journal section

• https://lpsa.swarthmore.edu/MtrxVibe/EigMat/MatrixEigen.html
• https://betterexplained.com/articles/hyperbolic-functions/
• https://byjus.com/maths/lyapunov-functions/
• https://www.jmlr.org/papers/volume25/23-1526/23-1526.pdf
• https://machinelearningmastery.com/a-gentle-introduction-to-the-jacobian/

• review questions: what is the state, what equilibrium or invariant set is the target, and what candidate scalar function would decrease along the specified dynamics? The notebook's model includes event-triggered updates, so behavior at events must be included rather than reasoning only between spikes.