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Focusing on crossing and product cubic systems, this monograph explores complex dynamics involving crossing-linear and self-quadratic product vector fields. It delves into singular equilibriums and hyperbolic flows, detailing transitions through various saddle types. The text highlights the interplay between simple equilibrium states and paralleled hyperbolic flows, addressing bifurcations such as parabola-saddles and third-order saddles. Through a rigorous analysis of nonlinear dynamics and singularities, it contributes to the understanding of these intricate mathematical structures.
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Two-dimensional Self and Product Cubic Systems, Vol. II, Albert C. J. Luo
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- 2024
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