Canards are characteristic phenomena of singularly perturbed systems with multiple time scales. Using the Bonhoeffer-van der Pol equations, we perform asymptotic analysis to obtain the parameter values where a canard solution exists. Although the system is two-dimensional, the numerical computations of the equations show a seemingly chaotic phenomenon at these parameter values. Consequently, high-precision numerical computations are employed to quantitatively evaluate both the convergent and divergent dynamics near a canard solution. The numerically produced fake chaos is attributed to insufficient precision of the stable dynamics.