FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca²⁺ NONLINEAR OSCILLATION MODEL WITH TIME DELAY

Frequency catastrophe is found in a cell Ca²⁺ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.