Introduction to the Modeling and Analysis of Complex Systems

48 CHAPTER 4. DISCRETE-TIME MODELS I: MODELING1.51.00.50.00.50 5 10 15 20 25 30Figure 4.2: Visual output of Code 4.11. This result is actually wrong.Code 4.13: oscillation-correct.pynextx = 0.5 * x + ynexty = -0.5 * x + yx, y = nextx, nextyHere we have two sets of state variables, x, y and nextx, nexty. We first calculate thenext state values and store them in nextx, nexty, and then copy them to x, y, which willbe used in the next iteration. In this way, we can avoid any interference between the statevariables during the updating process. If you apply this change to the code, you will get acorrect simulation result (Fig. 4.3).The issue of how to implement simultaneous updating of multiple variables is a commontechnical theme that appears in many complex systems simulation models, as wewill discuss more in later chapters. As seen in the example above, a simple solution is toprepare two separate sets of the state variables, one for now and the other for the immediatefuture, and calculate the updated values of state variables without directly modifyingthem during the updating.In the visualizations above, we simply plotted the state variables over time, but there is