Cokernel bundles and Fibonacci bundles

We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a resolution of the form $$0 \to \mathbb{C}^s \otimes E \xrightarrow{\mu} \mathbb{C}^t \otimes F \to C \to 0.$$ In this paper we prove that, under suitable conditions on $(E,F)$, a generic bundle with this form is either simple or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on $\mathbb{P}^2$ and we prove the stability when $E = \mathcal{O}$, $F = \mathcal{O}(1)$ and $C$ is an exceptional bundle on $\mathbb{P}^N$ for $N \geq 2$.