Ectopic activity, which is abnormal excitation in cardiac tissue, is one of the triggers for dangerous arrhythmia initiation. Recently, paradoxical onset of ectopic sources in the border zones between normal and damaged myocardium was reported in experimental (optogenetically modified monolayers of cardiomyocytes), computer simulations (simplified and ionic models) and theoretical studies [A. S. Teplenin, et al, “Paradoxical Onset of Arrhythmic Waves from Depolarized Areas in Cardiac Tissue Due to Curvature-Dependent Instability”, Phys. Rev. X 8, 021077 (2018)]. The study demonstrated that primary ectopic excitation takes place at areas of maximal curvature, such as corners of damaged tissue regions, in which, as stipulated in the paper, the stimulating (sourcing) coupling currents between cells are minimal and do not correspond to well-known source-sink relationship formulation for successful excitation of the neighboring normal tissue. This contradiction was reported for the first time and seems very interesting for further deeper investigations. In the work the authors utilized four models of different complexity, such as FitzHugh-Nagumo and Aliev-Panfilov simple two-variable models, ionic Majumder-Korhonen model for neonatal rat ventricular myocytes, and Ten Tusscher-Noble-Noble-Panfilov model for adult human ventricular myocytes. The models were modified to represent pathological properties of the damaged tissue. In our study, we use two-variable Mitchell-Schaeffer (2003) model and its modification (C. Corrado 2016), and four-variable Bueno-Orovio-Cherry-Fenton model (2008) of the human ventricular cells to investigate the possibility to obtain the paradoxical effect mentioned above in the popular minimal ionic models. We present some nonlinear analysis and comparison with classical FitzHugh-Nagumo model and attempt to clarify the mechanism of ectopic activity initiation in the border zones between normal and damaged cardiac tissue. Our study with the minimal ionic models can provide some additional insight into the prediction of possible triggers of dangerous cardiac arrhythmias.