This paper proposes finite-time (FT) and fixed-time (FXT) neurodynamic models with time-varying coefficients for solving inverse quasi-variational inequality problems (IQVIPs). Two projected models with time-dependent gains are developed to enhance convergence speed and transient performance. A nominal model establishes the equivalence between equilibrium points and IQVIP solutions. Under Lipschitz continuity and strong monotonicity assumptions, the existence, uniqueness, and global convergence of the proposed models are ensured. By employing Lyapunov stability theory, finite-time and fixed-time convergence of the continuous-time models are rigorously established, where explicit settling-time bounds independent of initial conditions are derived for the FXT case. Furthermore, the robustness of the proposed models under bounded disturbances is analyzed. To validate the theoretical findings, a discrete-time implementation based on the forward Euler method is developed. Numerical experiments demonstrate that all trajectories converge within a uniform upper bound, showing convergence behavior consistent with the fixed-time characteristics of the continuous-time model. Although the convergence time varies with initial conditions, it remains uniformly bounded, which is consistent with the fixed-time stability characteristics of the continuous-time model. The proposed framework provides a computationally efficient and scalable approach for solving IQVIPs, with potential applications in traffic equilibrium, communication networks, distributed control systems, and multi-agent coordination. Its adaptive structure and fixed-time convergence properties make it particularly suitable for real-time optimization in dynamic and uncertain environments.
Khan et al. (Mon,) studied this question.