Cokernel bundles and Fibonacci bundles

We are interested in those bundles $C$ on ${\mathbb{P}}^N$ which admit a resolution of the form $$0\to {\mathbb{C}}^s\otimes E\stackrel{\mu }{\to }{\mathbb{C}}^t\otimes F\to C\to 0.$$ 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 $N\ge 2$.