The chaos and NP-hardness conjecture for nonlinear systems

Let $({\cal P}_0)$ be the discretized nonlinear algebraic problem associated with a nonlinear dynamical system, and let $({\cal P})$ be the corresponding optimization problem with canonical dual $({\cal P}^d)$. A solution of $({\cal P}_0)$ is called chaotic when it exhibits the chaotic behavior intended by the source. Chaos and NP-hardness conjecture. The nonlinear system $({\cal P}_0)$ has chaotic solutions if and only if the optimization problem $({\cal P})$ is NP-hard, that is, if and only if its canonical dual $({\cal P}^d)$ is not solvable. The conjecture is presented as a proposed link between chaotic behavior in nonlinear dynamical systems and computational intractability; the source supplies no resolution.