Difference equation
= Difference equation
{title2=$z_{n+1}=F(z_n)$}
A <difference equation> relates values of a <sequence> at different indices, or its finite differences. A first-order autonomous system has the displayed form, with a scalar or vector state. Writing $z_{n+1}-z_n=F(z_n)-z_n$ gives its equivalent finite-difference form. Its <fixed point> stability is determined by the <Jacobian matrix> of the update and the <unit circle>, whereas a continuous-time <differential equation> uses the real parts of its linearized <eigenvalues>.