Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I

Beschreibung

This book, the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

• Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems;
• Provides a new research direction in nonlinear dynamics community;
• Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows.

This book is the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

Autor*in

Albert C. J. Luo

Themen in »Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I«

Constant and self-cubic systems Infinite-equilibriums Crossing-linear and self-cubic systems Two single-variable cubic systems Appearing bifurcations Inflection sinks, sources and saddles Up-down and down-up saddles Crossing-quadratic and self-cubic systems Third-order sink and source flows and saddle flows Third-order parabola flows and inflection flows Switching bifurcations Parabola sinks, sources and saddles Logarithmic and concave sinks and sources

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