In the study of dynamical systems there is the concept of 'sensitive dependence on initial conditions' (abbreviated SDIC) which says that two initially nearby trajectories will diverge exponentially quickly. This is known as the 'butterfly effect' in popular terminology.
More mathematically, take two trajectories $x_1(t)$, $x_2(t)$ and define the difference between them by $\delta x(t) = |x_1(t)-x_2(t)|$. We say that a system exhibits SDIC if for two initially nearby trajectories (in the sense that $\delta x(0)$ is small) we have
$\delta x(t) \sim e^{\lambda t}\delta x(0)$
for some $\lambda>0$, i.e. there is an exponentially fast divergence.
Your case is slightly more complicated because the initial sensitivity is to a parameter, rather than to the initial conditions. However, a dynamical system with state $x$ and a parameter vector $c$
$\dot{x}=f(x,c)$
can always be reimagined as a dynamical system in a larger state space by defining $y=(x,c)$ and setting
$\dot{y} = (f(x,c), 0)$
in which case you can apply the definitionto conclude that a system with exponential sensitivity to one of the parameters exhibits SDIC.