Difference, Not Differential

In Nonlinear Dynamics and Chaos, Steven H. Strogatz opens by naming two kinds of dynamical system: differential equations, which describe systems evolving in continuous time, and iterated maps, difference equations, which arise where time is discrete. Both are real; both are dynamics. Because differential equations are the more widely used in science and engineering, he makes a choice, and says so plainly: “Differential equations are used much more widely in science and engineering, and we shall therefore concentrate on them.”

, Steven H. Strogatz, Nonlinear Dynamics and Chaos, § 1.2, “The Importance of Being Nonlinear” (quoted verbatim; verified against the primary source)

Principia Attractum is where that road might have led had the other fork been taken. We concentrate on the one he set aside, the discrete one: not the next tick of a clock, but the next step of a structure’s own recursion, the next tik. Persistence, sovereignty, ignition, loss, everything here follows from that single change of foot.