Horseshoe chaos and topological entropy estimate in a simple power system (Q1021673)

A power system model described by the following differential equations is considered. \[ \begin{aligned} &\dot{\delta}_m = \omega,\\ &\dot{\omega} = c_1 \sin (\delta - \delta_m + c_2) \nu + c_3 \omega + c_4, \\ &\dot{\delta} = c_5 \nu^2 + c_6 \cos (\delta - \delta_m + c_7) \nu + c_8 \cos (\delta + c_9) \nu + c_{10} \nu + c_{11} Q_1 + c_{12}, \\ &\dot{\nu} = c_{13} \nu^2 + c_{15} \cos (\delta - \delta_m + c_{16}) \nu + c_{17} \cos (\delta + c_{18}) \nu + c_{19} \nu + c_{20} Q_1 + c_{21}.\end{aligned} \] Here \(c_i\) \((i = 1, \cdots , 21)\) are some constants. The existence of horseshoe chaos for the system is proved by means of topological horseshoe theory and computer computations. The essence of the arguments is to choose a cross section and study the dynamics of the corresponding Poincaré map to which the topological horseshoe theory can apply.