This paper investigates the temporal and spatiotemporal dynamics of a generalized Degn–Harrison chemical reaction model with nonlinear interaction rate \(\begin{aligned} \frac{k u^{p}v}{1+s u^{q}}. \end{aligned}\) The kinetic orders p and q separate the nonlinear activation in the u-channel from the inhibitory saturation in the denominator. Under positive parameter assumptions, we establish global-in-time existence, positivity and finite-time a priori bounds for the no-flux reaction–diffusion problem, and we derive boundedness and permanence estimates for the temporal kinetics. For the kinetic subsystem, the unique positive equilibrium is obtained explicitly, and its local stability is characterized completely by the trace and determinant of the Jacobian. A conditional global asymptotic stability result is proved in the monotone-rate subcase. At the loss of temporal stability, an explicit Hopf threshold is derived, the transversality condition is verified, and the first Lyapunov coefficient is evaluated through Kuznetsov’s multilinear normal-form formula. After diffusion is restored, the Turing instability conditions are written in terms of the Neumann spectrum and the kinetic Jacobian coefficients, giving a computable instability band and critical wave number. High-resolution numerical experiments show Hopf bifurcation diagrams, stable limit cycles, square-root Hopf scaling, dispersion curves, stationary Turing patterns, and transient breathing spatiotemporal states. The comparison with the classical choice \((p,q)=(1,2)\) demonstrates that stronger inhibitory kinetics can shift the Hopf threshold and open a genuine Turing window that is absent for the corresponding classical parameter regime.
