Enzymatic reaction networks capable of generating complex spatiotemporal dynamics are not only the basis of essential biological processes, but also the basic units of synthetic systems with autonomous, adaptive and programmable behaviours. Activation and inhibition have been usually considered as indispensable interactions for the construction of such networks. Here we present an enzymatic reaction network that consists of a flavin adenine dinucleotide-dependent oxidoreductase and a peroxidase that can generate tunable complex dynamics. These include charging/discharging, rectangular and parabolic pulses in a closed system, which are based on delayed and self-adapting substrate competition, rather than on activation or inhibition. Additionally, this system can spontaneously form visible spatiotemporal patterns that arise from reaction-driven Rayleigh–Bénard convection. This work demonstrates that substrate competition could be an alternative path towards constructing biochemical networks with complex dynamics.