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Chaotic systems are complex, constantly evolving systems that display unpredictable behavior due to their intrinsic randomness and sensitivity to initial conditions. They are characterized by the butterfly effect, where minor changes in starting conditions can lead to significantly different outcomes. Analysis of nonlinear behavior and chaotic control of the Duffing-Holmes system is investigated in this research and an optimal intelligent backstepping controller is designed to eliminate the chaotic movement outside normal behavior. The backstepping technique involves parameters that must be positive. Incorrectly choosing these parameters causes irrational behavior or system instability. In this research, a Deep Neural Network (DNN) is merged with the Backstepping method (DNN + Backstepping) To identify the suitable and optimal values for the controller parameters, one of the key benefits of the proposed control system is its ability to rapidly control chaos within a short time using a limited control signal. Numerical results demonstrate the effectiveness of this method in eliminating chaos from the Duffing-Holmes system. The results demonstrate a decrease of about 1 s in convergence time and an approximately 85% reduction in control signal amplitude. Moreover, the final convergence value of the objective function using the proposed method is significantly lower than unified particle swarm optimization (UPSO). In both of the methods, the state variables are converged to zero. By optimally tuning backstepping parameters via DNN, the method achieves state convergence to zero in 3 s—1 s faster than UPSO-Backstepping (4 s)—while reducing control signal amplitude by ∼85% (from peaks of ±0.6 to ±0.03) and minimizing the objective function by 99% (0.0002 vs. 0.31). • Developing a novel Deep Neural Network–Backstepping (DNN–Backstepping) control scheme that integrates classical backstepping control with deep learning for the stabilization of chaotic nonlinear systems. • Achieving notable performance improvements in controlling the Duffing–Holmes chaotic oscillator, reducing the convergence time to 3 s, which is 1 s faster than the Unified Particle Swarm Optimization (UPSO)–based method. • Demonstrating an 85% reduction in control signal amplitude, resulting in more efficient control actions with lower energy consumption. • Obtaining a noticeable reduction in the objective function value compared to the UPSO approach, indicating enhanced optimization efficiency and improved control robustness. • Enabling fast, model-independent online adaptation of controller parameters, effectively addressing key challenges associated with nonlinear chaotic dynamics. • Providing comprehensive simulation results that confirm the applicability of the proposed controller in practical systems, including mechanical vibration control, electrical circuits, secure communication systems, and financial system stabilization. • Identifying limitations related to the interpretability of neural network–based controllers due to their black-box nature and outlined future research directions focused on incorporating explainable AI techniques to enhance control transparency.