This paper investigates the dynamic behavior of the (3+1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov (NLEQZK) equation, focusing on soliton solutions, chaotic phenomena, bifurcation, sensitivity, and stability using planar dynamical system theory. The generalized Arnous method is employed to derive soliton solutions, which include hyperbolic, rational, and logarithmic forms. These solutions are visualized using 3D surface graphs and line graphs with appropriate parameter values. The governing equation is derived via Galilean transformation for bifurcation analysis. Chaotic behavior is analyzed by introducing a perturbed term and using Poincaré maps, time series, 2D and 3D phase portraits. The Runge–Kutta method is used for sensitivity analysis, confirming the system's sensitivity to initial conditions. The study contributes insights into nonlinear dynamical systems and soliton theory. Nonlinear evolution equations (NLEEs) are important mathematical tools for modeling complex nonlinear phenomena in various fields. Soliton solutions, which maintain their shape and speed, are crucial for understanding wave phenomena. Various analytic methods have been developed to find exact solutions of NLEEs, including the auxiliary equation method, modified extended direct algebraic method, and others. Bifurcation analysis helps understand qualitative changes in system solutions as parameters vary. Chaos, characterized by uncertainty and unpredictability, is a common phenomenon in nonlinear systems. Understanding chaotic behavior is important for predicting and controlling real-world systems. The NLEQZK equation is a notable example of a nonlinear partial differential equation used to model complex systems in quantum mechanics, fluid dynamics, and nonlinear wave propagation. The study provides valuable insights into the behavior of nonlinear systems and the role of soliton solutions in understanding complex dynamics.This paper investigates the dynamic behavior of the (3+1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov (NLEQZK) equation, focusing on soliton solutions, chaotic phenomena, bifurcation, sensitivity, and stability using planar dynamical system theory. The generalized Arnous method is employed to derive soliton solutions, which include hyperbolic, rational, and logarithmic forms. These solutions are visualized using 3D surface graphs and line graphs with appropriate parameter values. The governing equation is derived via Galilean transformation for bifurcation analysis. Chaotic behavior is analyzed by introducing a perturbed term and using Poincaré maps, time series, 2D and 3D phase portraits. The Runge–Kutta method is used for sensitivity analysis, confirming the system's sensitivity to initial conditions. The study contributes insights into nonlinear dynamical systems and soliton theory. Nonlinear evolution equations (NLEEs) are important mathematical tools for modeling complex nonlinear phenomena in various fields. Soliton solutions, which maintain their shape and speed, are crucial for understanding wave phenomena. Various analytic methods have been developed to find exact solutions of NLEEs, including the auxiliary equation method, modified extended direct algebraic method, and others. Bifurcation analysis helps understand qualitative changes in system solutions as parameters vary. Chaos, characterized by uncertainty and unpredictability, is a common phenomenon in nonlinear systems. Understanding chaotic behavior is important for predicting and controlling real-world systems. The NLEQZK equation is a notable example of a nonlinear partial differential equation used to model complex systems in quantum mechanics, fluid dynamics, and nonlinear wave propagation. The study provides valuable insights into the behavior of nonlinear systems and the role of soliton solutions in understanding complex dynamics.