Figure 2From: The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse ProblemEigenvalues of the Jacobian matrix correspond to intersections of the two function and . This Figure illustrates how a stable fixed point is destabilized by a time delay Ï„. (a) For , is a constant function, and the Jacobian matrix has two negative real eigenvalues and . (b) For , the function is a strictly increasing function that approaches 0 exponentially. Thus, increasing Ï„, the two real eigenvalues coalesce to a pair of complex conjugate eigenvalues, whose real parts eventually become positive. (c) A further increase in Ï„ leads to a new osculation point of and at a value . This is positive and real, and hence corresponds to an unstable fixed point. (d) For , the two eigenvalues approach the values and .Back to article page