Clustered spots in the FitzHugh–Nagumo system

We construct clustered spots for the following FitzHugh–Nagumo system: 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 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 and the following holds: (i) The center of the cluster approaches a hotspot point Q0 Ω. (ii) Set . Then approaches an optimal configuration of the following problem: (*) Given K points Q1,…,QK R2 with minimum distance 1, find out the optimal configuration that minimizes the functional .