Thermal feedback as a kinetic control mechanism in reaction–diffusion pattern formation

Pattern formation in reaction-diffusion systems is traditionally analyzed under isothermal assumptions, overlooking the dynamical role of temperature in systems where reactions generate and dissipate heat. Here, we investigate non-isothermal reaction-diffusion dynamics by coupling activator-inhibitor kinetics to a dynamically evolving temperature field that modulates reaction rates through Arrhenius-type dependencies. This coupling introduces an additional feedback mechanism that influences stability and pattern selection. Through analytical and numerical investigations of the phenomenological Schnakenberg and chemically motivated chlorine dioxide-iodine-malonic acid models, we demonstrate that thermal feedback systematically reshapes the stability landscape by modifying dispersion relations, shifting instability boundaries, and regulating the characteristic wavelength of the emergent patterns. Beyond these linear effects, thermal coupling can induce or suppress diffusion-driven instability and continuously reorganize nonlinear spatial morphologies depending on the operating point in parameter space. These results establish thermal-kinetic coupling as a general mechanism for controlling pattern formation across different reaction kinetics while highlighting the model-dependent nature of the resulting nonlinear dynamics.