A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks

We propose a nonlinear wetware-inspired dynamical framework governed by a two-parameter K–R structure, where the excitation parameter \(\:K\:\)and the regulation parameter \(\:R\:\)provide interpretable control over system plasticity and stabilization. The model incorporates biologically motivated saturation nonlinearities and is analyzed using a non-quadratic Lyapunov function specifically tailored to the system dynamics. Rigorous analysis establishes global asymptotic stability of the equilibrium for all admissible initial conditions and parameter ranges. To validate the theoretical results, extensive numerical simulations are conducted. State trajectory analyses demonstrate robust global convergence from widely separated initial conditions under variations of \(\:K\), \(\:R\), and nonlinear gain parameters. The Lyapunov function is shown to decay monotonically along all simulated trajectories, providing strong numerical confirmation of the analytical stability guarantees. Phase-portrait analysis further illustrates how excitation gain reshapes the vector field while preserving global stability and a unique equilibrium. Beyond qualitative validation, a quantitative convergence benchmark is introduced through settling-time analysis. Numerical experiments reveal a clear dependence of convergence speed on the excitation–regulation trade-off, showing that the K–R framework enables explicit and measurable control of stabilization dynamics. In particular, increasing excitation strength accelerates convergence after an initial regime, highlighting a nontrivial performance–stability interaction induced by nonlinear saturation. Overall, the results demonstrate that the proposed K–R framework unifies global Lyapunov stability, nonlinear wetware modeling, and quantitative convergence characterization within a single, interpretable dynamical system. This combination provides a mathematically rigorous and computationally reproducible foundation for analyzing stability–plasticity trade-offs in nonlinear neural and wetware-inspired systems.