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Nt1310 Unit 4 Test Paper

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Plot a family of curves (use at least 20 values of K; you will probably need to use more) of P_(steady state) against iteration number to illustrate your findings. This paper comprises an appreciation of data representation, its visualization, an outline description of behavior, plus an indication of the use of the equation in engineering. Given that P_0=0.35 (the starting value for Pn) conducting 30 iterations on the first family of curves when 0.5≤K≤1 I’ve noticed that the system values increases from its initial value until it reaches a steady state on 1 smoothly without oscillating around it. The below figure indicates the 5 values I’ve chosen for K between 0.5 and 1 and shows how smooth the transition is from the original value to 1. …show more content…

Define the δ and α values and their associated mathematical functions. Using Excel to produce 2,000 iterations of the given Logistic Equation: P_(N+1)= P_N+ KP_N (1-P_N) When plotting the last 50 iterations of Psteady state against 0.5 < K < 3 the following diagram appears: Figure 8 Bifurcation Diagram The Bifurcation diagram also called the logistic map, shows the region of all possible values of the logistic equation. The relative simplicity of the logistic map makes it a widely used point of entry into a consideration of the concept of chaos. By using this diagram we can define the doubling cycles with its associated K values, as I mentioned in the previous part a) the region of steady state of one value exists when 0.5 < K < 2 afterwards it stars doubling exponentially around the region when K is between 2 and 2.45 and the system would be giving two values of P. Zooming into our logistic map for us to be able to determine the next doubling, the below figure shows our system when K is between 2.4 and 2.7 in the Bifurcation diagram. Figure 9 Bifurcation when 2.4< 1, and c is the limit of growth.

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