Tag
Differential Equations
Entries tagged differential equations.
3 entries
Differential equations as rules of evolution
A differential equation describes a system not by giving its state directly but by giving the rule for how that state changes right now, based only on what the state is right now.
6 min
ConceptFirst-order dynamics
A first-order dynamical system is one whose rate of change depends only on its current value, and that single restriction is strong enough to force the state toward exactly one of three long-term fates: unbounded growth, decay to zero, or settling at equilibrium.
6 min
ConceptSecond-order dynamics
A second-order dynamical system is one whose evolution rule constrains not the rate of change of its state but the rate of change of that rate, which is what allows a system to overshoot, reverse, and oscillate instead of only growing, decaying, or settling.
7 min