Coupling chaotic and periodic behaviour in cell suspensions

6 Coupling chaotic and periodic behaviour in cell suspensions 

The parameter that is chosen to differ for the two pure populations is either the net rate of ATP supply within the cells (v), or the total activity of phosphodiesterase (IcJ. The values of the two parameters for populations 1 and 2 will be denoted by Vj, and V2, fce2. respectively. 

Period-doubling route to chaos as a function of the relative proportions of chaotic and periodic cells 

For simplicity, let us consider first that the two populations differ only by parameter v, which measures the net, constant input of ATP into the adenylate cyclase reaction site within the cells. To determine the effect of coupling chaotic with periodic behaviour, we consider the situation where population 1 has a value of Vj corresponding to chaotic behaviour while the second population has a value of Vj corresponding to periodic oscillations. The question that arises is how the dynamics of the mixed suspension varies as a function of the relative proportions F, and F2 = 1- Fi of the two populations. 

when the proportion of chaotic cells in the mixed suspension is progressively increased from 0 to 100%, the dynamics changes from periodic to chaotic through a sequence of period-doubling bifurcations. What is of interest is that such a well-known route to chaos is encountered here as a function of the relative proportions of periodic and chaotic cells upon mixing such populations in a common suspension. 

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