The latest reddish contour in the Fig 1C reveals the newest combined advancement out-of an impact and energy regarding a flourishing relationship: the required quantity of work is higher than the most used peak c* = 0
Fig 1C shows the vector field of the feeling-effort dynamics (15) computed using a Runge-Kutta numerical scheme. It shows a particular example of the phase portrait of the 1D couple’s problem (see Fig 3 in ). The optimal trajectory (c ? (t), x ? (t)) for x0 = 3 computed by the algorithm is plotted in red. The trajectory lies on the stable manifold and approaches the equilibrium levels as t increases, in accordance with the computation in . 2 and increases over time, while the feeling –initially high– declines. Eventually, both variables enter a stationary regime in which the feeling is sufficiently gratifying and the effort remains beyond the favorite level.
The new feedback plan (SM1) takes the latest calculated worth c ? (0) because initial reputation so you’re able to produce the new open-circle provider with the “lovebirds problem” experienced during the : because of the initially effect x(0), the fresh formula discovers the initial effort c(0) therefore the entire trajectory (c ? (t), x ? (t)) lies on the fresh new stable manifold away from (15). The fresh viewpoints data away from Fig 1A stretches the newest open-cycle numerical study out of .