The inverse problem of parameter estimation for Duffing oscillator, a chaotic dynamical system well known in engineering is solved using quantum-inspired evolutionary algorithm, differential evolution and genetic algorithms. The paper focuses on such combination of parameters that produce periodic responses instead of purely chaotic responses. The feature set used is a set of displacement values of the first five Poincaré points, after ignoring transient effects. All approaches correctly identify the target set of parameters as producing the given response; however, depending on the fitness landscape some parameters are more difficult to identify than others especially when using the canonical genetic algorithm. This paper is also the first to investigate the quantum-inspired evolutionary algorithm for such parameter identification problems.