Complete Formula Sheet

Mathematical Modeling · Axiom Academy

FORMULA SHEET Complete Formula Sheet Mathematical Modeling - Comprehensive Quick Reference for All Units n = number of variables, k = number of dimensions Measures relative change in output per relative change in parameter where P is the transition matrix K = maximum sustainable population PREDATOR-PREY (LOTKA-VOLTERRA) Stable if: tr(J) < 0 and det(J) > 0 Unstable if: det(J) < 0 (saddle) Unstable if: tr(J) > 0 and det(J) > 0 where p = prob. of step right, q = 1 - p where lambda = birth rate, mu = death rate Stochastic models capture randomness in individual events, important for small populations. Requires: D_v >> D_u (activator-inhibitor) SE = standard error of parameter estimate Lower CV error indicates better generalization.

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