Two-dimensional Self and Product Cubic Systems, Vol. I

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Focusing on crossing and product cubic systems, this monograph delves into self-linear and crossing-quadratic product vector fields. Dr. Luo explores singular equilibrium series characterized by inflection-source and parabola-source flows, detailing the dynamics of networks with hyperbolic flows. The study emphasizes the nonlinear dynamics and singularities of these systems, highlighting the bifurcations that arise within them. This work is part of a larger series on Cubic Dynamical Systems, contributing to the understanding of complex mathematical behaviors in this field.