On nonlinear singularly perturbed problems in biology
The paper studies a quasi-linear problem with singular perturbation, presented by means of a system of ordinary differential equations. The problem can be applied to model the heartbeat and nerve impulse propagation. The authors develop a constructive algorithm that can be used for evaluating the eigenvalues of the system matrix and indicate conditions of its applicability. They also find relations among given parameters under which the matrix can be reduced to a diagonal matrix. Conditions under which the trivial solution of the problem is asymptotically stable are presented. Two applied examples that illustrate the results obtained conclude the paper.