 (WSD) A system characterized  by \(\bJ(\bx(t))\)  has the property of weak sensitive dependence on its initial  conditions if and only if  \(\exists \varepsilon \gt 0\) \(\forall \bx(0)\) \(\forall \delta \gt 0\)  \(\exists t\gt 0\) \(\exists \by(0)\), \(\abs{\bx(0) - \by(0)} \lt \delta\) and   \(\abs{\bJ(\bx(t)) - \bJ(\by(t))} \gt \varepsilon.\) 