When y nears 1, your differential equation system becomes what is known as 'stiff'. Even though the ideal solution is a perfectly smooth and regular function, the sizes of steps required in solving the corresponding differential equation system numerically become increasingly small. Look at it this way. When y attains a value of one, the differential equation dictates that the derivative dy/dt should be zero there. What is to prevent it from remaining fixed at y = 1 from that point on, or wandering off in any of a number of different directions? It is clearly a point of instability as far as the differential equation is concerned. This situation is not caused by the complex values you are seeing but lies in the very nature of the differential equation at this point. Read about this phenomenon at:
http://en.wikipedia.org/wiki/Stiff_equation
