# Research on the Vehicle Steering and Braking Stability Region
## 3 Solution of Equivalent Equilibrium Point
### Analysis of Bifurcation Characteristics of Equilibrium Point
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(T_{b}\)} & \multicolumn{6}{c}{Vehicle Dynamics Equilibriums} & \multicolumn{6}{c}{**Rate of System Variable Change**} & \multirow{2}{*}{**Fitness**} \\ \cline{2-2} \cline{4-11}  & \(v_{y}\) & \(\omega\) & \(v_{x}\) & \(\omega_{f}\) & \(\omega_{r}\) & \(\dot{v}_{y}\) & \(\dot{\omega}\) & \(\dot{v}_{x}\) & \(\dot{\omega}_{f}\) & \(\dot{\omega}_{r}\) & \\ \cline{2-11}  & (m/s) & (rad/s) & (m/s) & (rad/s) & (rad/s) & & \(\dot{v}_{y}\) & \(\dot{\omega}\) & \(\dot{v}_{x}\) & \(\dot{\omega}_{f}\) & \(\dot{\omega}_{r}\) & \\ \hline
60.48 & 1.9081 & \(-\)0.0804 & 29.9688 & 132.8727 & 133.2487 & 0.0000 & 0.0000 & \(-\)0.1343 & 0.0000 & \(-\)0.0001 & 0.1345 \\
120.96 & 1.9501 & \(-\)0.0798 & 29.9851 & 131.9924 & 132.7804 & 0.0000 & 0.0000 & \(-\)0.1367 & 0.0001 & 0.0000 & 0.1368 \\
181.44 & 2.0027 & \(-\)0.0789 & 29.9691 & 131.0290 & 132.1721 & 0.0000 & 0.0000 & \(-\)0.1392 & 0.0000 & 0.0000 & 0.1392 \\
241.92 & 2.0624 & \(-\)0.0777 & 29.9596 & 130.1154 & 131.5962 & 0.0000 & 0.0000 & \(-\)0.1414 & 0.0000 & 0.0001 & 0.1418 \\
302.40 & 2.1372 & \(-\)0.0765 & 29.9692 & 129.2572 & 131.0944 & 0.0000 & \(-\)0.0030 & \(-\)0.1452 & 0.0000 & 0.0000 & 0.1483 \\
362.88 & 2.2020 & \(-\)0.0749 & 29.9694 & 128.3242 & 130.5514 & 0.0000 & 0.0000 & \(-\)0.1471 & 0.0000 & 0.0000 & 0.1471 \\
423.36 & 2.2848 & \(-\)0.0732 & 29.9698 & 127.2831 & 129.9736 & 0.0000 & 0.0000 & \(-\)0.1499 & 0.0001 & 0.0000 & 0.1500 \\
483.84 & 2.3826 & \(-\)0.0714 & 29.9698 & 126.0794 & 129.3452 & 0.0000 & 0.0000 & \(-\)0.1532 & 0.0000 & 0.0000 & 0.1532 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Vehicle dynamics partial values for another unstable equilibrium point. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(T_{b}\)} & \multicolumn{6}{c}{Vehicle Dynamics Equilibriums} & \multicolumn{6}{c}{**Rate of System Variable Change**} & \multirow{2}{*}{**Fitness**} \\ \cline{2-2} \cline{4-11}  & \(v_{y}\) & \(\omega\) & \(v_{x}\) & \(\omega_{f}\) & \(\omega_{r}\) & \(\dot{v}_{y}\) & \(\dot{\omega}\) & \(\dot{v}_{x}\) & \(\dot{\omega}_{f}\) & \(\dot{\omega}_{r}\) & \\ \cline{2-11}  & (m/s) & (rad/s) & (m/s) & (rad/s) & (rad/s) & \(\dot{v}_{y}\) & \(\dot{\omega}\) & \(\dot{\omega}\) & \(\dot{v}_{x}\) & \(\dot{\omega}_{f}\) & \(\dot{\omega}_{r}\) & \\ \hline
272.16 & \(-\)1.0630 & 0.0709 & 29.9855 & 129.7561 & 132.2881 & 0.0000 & 0.0037 & \(-\)0.0919 & 0.0000 & 0.0000 & 0.0956 \\
322.56 & \(-\)1.2107 & 0.0732 & 29.9939 & 128.9161 & 131.9043 & 0.0000 & \(-\)0.0014 & \(-\)0.1057 & 0.0000 & 0.0000 & 0.1071 \\
372.96 & \(-\)1.3626 & 0.0746 & 29.9676 & 127.8544 & 131.3307 & 0.0000 & 0.0001 & \(-\)0.1188 & 0.0000 & 0.0000 & 0.1188 \\
423.36 & \(-\)1.4954 & 0.0745 & 29.9688 & 126.8547 & 130.8688 & 0.0000 & 0.0000 & \(-\)0.1286 & 0.0000 & 0.0000 & 0.1286 \\
473.76 & \(-\)1.6361 & 0.0738 & 29.9702 & 125.7211 & 130.3674 & 0.0000 & 0.0000 & \(-\)0.1378 & 0.0000 & 0.0000 & 0.1378 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Vehicle dynamics partial values for one unstable equilibrium point.