Two-dimensional Crossing-Variable Cubic Nonlinear Systems, Vol IV

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The book delves into the theory of crossing-cubic nonlinear systems, examining various vector fields such as constant, crossing-linear, crossing-quadratic, and crossing-cubic. It details the dynamics of these systems, including 1-dimensional flows like parabola and inflection flows, as well as more complex equilibriums like saddle and center points. It also explores higher-order dynamics, including third-order saddles and centers, and discusses the formation of homoclinic orbits and networks, providing a comprehensive framework for understanding these nonlinear systems.