Albert C. J. Luo Pořadí knih

Focusing on the theoretical framework of product-cubic nonlinear systems, this monograph delves into the dynamics of systems characterized by constant and single-variable linear vector fields. It explores hyperbolic flows and their interactions with cubic product systems, detailing bifurcations and equilibrium points. The text examines both connected and separated hyperbolic flows, highlighting the behavior of inflection-source and sink equilibria in relation to switching bifurcations, providing a comprehensive analysis of complex flow dynamics in these mathematical systems.

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.

Focusing on cubic nonlinear systems, this monograph introduces a systematic theory centered around single-variable vector fields. It delves into 1-dimensional flow singularities and bifurcations, showcasing previously unexplored bifurcations in 2-dimensional cubic systems. The text covers third-order source and sink flows, as well as parabola flows, highlighting the significance of infinite-equilibriums in switching bifurcations. Additionally, it details various bifurcations, including saddle flows and inflection flows, providing a comprehensive analysis of these complex systems.

Focusing on product-cubic nonlinear systems, this volume delves into the dynamics of two crossing-linear and self-quadratic product vector fields. It explores equilibrium and flow singularities, emphasizing bifurcations, including appearing and switching types. The text details double-saddle equilibria related to saddle source and saddle-sink bifurcations, along with a network of saddles. Additionally, it presents infinite-equilibriums associated with switching bifurcations, offering insights into complex dynamic behaviors and their implications.

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.

Focusing on cubic nonlinear systems, this monograph delves into the intricacies of single-variable vector fields, particularly those with crossing variables. It explores 1-dimensional flow singularities and bifurcations, presenting novel insights into the switching bifurcations within 2-dimensional cubic systems. The text details third-order parabola flows and saddle flows, highlighting the significance of infinite equilibria and various flow types, including inflection flows and saddle flows, in understanding the dynamics of these systems.

Focusing on the intricate dynamics of polynomial systems, this monograph explores limit cycles and homoclinic networks, addressing Hilbert's sixteenth problem. It examines the equilibrium properties in planar polynomial systems, determining first integral manifolds and developing bifurcation theory related to homoclinic networks. The work identifies the maximum numbers of centers, saddles, sinks, and sources, contributing to a deeper understanding of global dynamics. This resource is invaluable for graduate students and researchers in mathematics and engineering fields.

Focusing on nonlinear dynamics, this monograph delves into cubic dynamical systems characterized by product-cubic and self-univariate quadratic vector fields. It explores equilibrium singularities and bifurcation dynamics, highlighting the emergence of saddle-source and double-saddle equilibriums. Additionally, the text discusses the interplay between saddle, sink, and source bifurcations, as well as infinite-equilibriums related to switching bifurcations, providing a comprehensive analysis for advanced studies in this area.

The book explores a comprehensive theory of self-independent cubic nonlinear systems, detailing various configurations of vector fields, including self-cubic, constant, self-linear, and self-quadratic types. It examines the dynamical systems' behavior, highlighting the presence of one-dimensional flows such as sources, sinks, and saddles, as well as more complex third-order flows. Additionally, it discusses the formation of homoclinic orbits and networks related to these flows, providing a deep insight into the dynamics and equilibria of these systems.

Focusing on the intricate dynamics of singularity and equilibrium networks, this monograph delves into 1-dimensional flows within quadratic and cubic systems. It categorizes equilibriums into sources, sinks, and saddles, detailing their behaviors with counter-clockwise and clockwise centers. The author explores various types of flows, including hyperbolic and parabola flows, and discusses bifurcations related to singular equilibriums. Additionally, it introduces new concepts and analytical techniques, making it a valuable resource for understanding complex mathematical phenomena.