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Archimedes' optimization algorithm (AOA) is a recently proposed physics-based optimization algorithm inspired by Archimedes' Principle. However, for optimization of complex engineering problems, it shows slow convergence and can easily fall into local minima. Chaotic maps have non-repeatability properties they can effectively scan the search space with fast convergence in optimization algorithms. In this study, knacks of physics-based optimization along with chaotic maps are exploited for the parameter estimation of autoregressive exogenous (ARX), nonlinear input ARX (NI-ARX), LD-Didactic temperature process plant models and electrically stimulated muscle model. Ten chaotic maps have been applied to AOA. The fitness function of both models is constructed based on the square error between true and estimated response. The chaotic variants indicate that AOA with a chaotic Circle map (CAOA2) gives the best performance in terms of accuracy and convergence against reptile search heuristics, sine cosine optimization approach, harris hawks optimizer (HHO) and whale optimization algorithm (WOA) for different variations of generation and noise levels. Statistics based on mean square error, convergence plots, statistical plots, Taguchi test, average fitness, t -test, and Friedman test for repeated measures approve the reliability of CAOA2 for parameter estimation of ARX, NI-ARX, LD-Didactic temperature process plant models and electrically stimulated muscle model. [ABSTRACT FROM AUTHOR]