Two-Dimensional Two-Product Cubic Systems, Vol I: Different Product Structure Vector Fields (2024)

This book is the ninth of 15 related monographs, discusses a two product-cubic dynamical system possessing different product-cubic structures and the equilibrium and flow singularity and bifurcations for appearing and switching bifurcations. The appearing bifurcations herein are parabola-saddles, saddle-sources (sinks), hyperbolic-to-hyperbolic-secant flows, and inflection-source (sink) flows. The switching bifurcations for saddle-source (sink) with hyperbolic-to-hyperbolic-secant flows and parabola-saddles with inflection-source (sink) flows are based on the parabola-source (sink), parabola-saddles, inflection-saddles infinite-equilibriums. The switching bifurcations for the network of the simple equilibriums with hyperbolic flows are parabola-saddles and inflection-source (sink) on the inflection-source and sink infinite-equilibriums. Readers will learn new concepts, theory, phenomena, and analysis techniques.

- Two-different product-cubic systems

- Hybrid networks of higher-order equilibriums and flows

- Hybrid series of simple equilibriums and hyperbolic flows

- Higher-singular equilibrium appearing bifurcations

- Higher-order singular flow appearing bifurcations

- Parabola-source (sink) infinite-equilibriums

- Parabola-saddle infinite-equilibriums

- Inflection-saddle infinite-equilibriums

- Inflection-source (sink) infinite-equilibriums

- Infinite-equilibrium switching bifurcations.