Clustered spots in the FitzHugh-Nagumo system

We construct clustered spots for the following FitzHugh-Nagumo system:ε2Δu+f(u)-δv=0inΩ,Δv+u=0inΩ,u=v=0on∂Ω,where Ω is a smooth and bounded domain in R2. More precisely, we show that for any given integer K, there exists an εK>0 such that for 0<ε<εK,εm′⩽δ⩽εm for some positive numbers m′,m, there exists a solution (uε,vε) to the FitzHugh-Nagumo system with the property that uε has K spikes Q1ε,…,QKε and the following holds: