The epidermal growth factor receptor (EGFR) belongs to the receptor tyrosine kinase (RTK) superfamily and is involved in regulating cell proliferation, differentiation and motility. Growth factor binding induces receptor oligomerization at the plasma membrane, which leads to activation of the intrinsic RTK activity and trans-phosphorylation of tyrosine residues in the intracellular part of the receptor. These residues are docking sites for proteins containing Src homology domain 2 and phosphotyrosine-binding domains that relay the signal inside the cell. In response to EGF attached to beads, lateral propagation of EGFR phosphorylation occurs at the plasma membrane, representing an early amplification step in EGFR signalling. Here we have investigated an underlying reaction network that couples RTK activity to protein tyrosine phosphatase (PTP) inhibition by reactive oxygen species. Mathematical analysis of the chemical kinetic equations of the minimal reaction network detects general properties of this system that can be observed experimentally by imaging EGFR phosphorylation in cells. The existence of a bistable state in this reaction network explains a threshold response and how a high proportion of phosphorylated receptors can be maintained in plasma membrane regions that are not exposed to ligand.