Research Article

Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow

Figure 1

The phase portrait of the four asymptotically stable fixed points at ; the first asymptotically stable fixed point (top left) is obtained using the following initial conditions: = (−0.8275, −0.4703, 0.7234, −2.3355, −0.122, −3.599, 0.4255); the second asymptotically stable fixed point (bottom right) is obtained using the initial conditions: = (0.8275, −0.4703, 0.7234, 2.3355, −0.122, 3.599, −0.4255) = (−0.8275, −0.4703, 0.7234, −2.3355, −0.122, −3.599, 0.4255); the third asymptotically stable fixed point (top right) is generated using the initial conditions: = (0.8275, 0.4703, 0.7234, −2.3355, 0.122, −3.599, 0.4255) = (0.8275, −0.4703, 0.7234, 2.3355, −0.122, 3.599, −0.4255); the fourth asymptotically stable fixed point (bottom left) is generated using the initial conditions: = (−0.8275, 0.4703, 0.7234, 2.3355, 0.122, 3.599, −0.4255) = (0.8275, −0.4703, 0.7234, 2.3355, −0.122, 3.599, −0.4255).